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A graph-theoretic approach to ring analysis: Dominant metric dimensions in zero-divisor graphs.
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- cautionDOI registered: No matching Crossref record was present in this response.
- cautionDOI resolves: No matching Crossref record was present in this response.
- not scoredDirectory of Open Access Journals: No matching DOAJ record was present in this response. No allow-list match; this is not evidence of low credibility.
- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: No retraction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch expression of concern: No expression of concern notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch correction: No correction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch reinstatement: No reinstatement notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- supportingOpen access status: Normalized open-access status: open.
- not scoredPublication license: Not checked or no result supplied; no credibility inference made.
- not scoredPublication version: A publication version was supplied but is not scored.
- cautionMetadata completeness: 5 of 6 scored descriptive metadata groups are present; missing fields increase uncertainty.
Harary index of the zero divisor graph of upper triangular matrices.
limited evidence
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- cautionDOI registered: No matching Crossref record was present in this response.
- cautionDOI resolves: No matching Crossref record was present in this response.
- not scoredDirectory of Open Access Journals: No matching DOAJ record was present in this response. No allow-list match; this is not evidence of low credibility.
- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: No retraction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch expression of concern: No expression of concern notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch correction: No correction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch reinstatement: No reinstatement notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- supportingOpen access status: Normalized open-access status: open.
- not scoredPublication license: Not checked or no result supplied; no credibility inference made.
- not scoredPublication version: A publication version was supplied but is not scored.
- cautionMetadata completeness: 5 of 6 scored descriptive metadata groups are present; missing fields increase uncertainty.
Fourier-based chemometric resolution of the FOLFOX regimen through digital filtering with poly-metric sustainability assessment.
limited evidence
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- cautionDOI registered: No matching Crossref record was present in this response.
- cautionDOI resolves: No matching Crossref record was present in this response.
- not scoredDirectory of Open Access Journals: No matching DOAJ record was present in this response. No allow-list match; this is not evidence of low credibility.
- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: No retraction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch expression of concern: No expression of concern notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch correction: No correction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch reinstatement: No reinstatement notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- supportingOpen access status: Normalized open-access status: open.
- not scoredPublication license: Not checked or no result supplied; no credibility inference made.
- not scoredPublication version: A publication version was supplied but is not scored.
- cautionMetadata completeness: 5 of 6 scored descriptive metadata groups are present; missing fields increase uncertainty.
Eco-sustainable organic solvent-free spectrophotometric method for the concurrent determination of a ternary pharmaceutical mixture.
limited evidence
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- cautionDOI registered: No matching Crossref record was present in this response.
- cautionDOI resolves: No matching Crossref record was present in this response.
- not scoredDirectory of Open Access Journals: No matching DOAJ record was present in this response. No allow-list match; this is not evidence of low credibility.
- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: No retraction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch expression of concern: No expression of concern notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch correction: No correction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch reinstatement: No reinstatement notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- supportingOpen access status: Normalized open-access status: open.
- not scoredPublication license: Not checked or no result supplied; no credibility inference made.
- not scoredPublication version: A publication version was supplied but is not scored.
- cautionMetadata completeness: 5 of 6 scored descriptive metadata groups are present; missing fields increase uncertainty.
A Study on the Structure of Ideal-Based Non-Zero Divisor Graphs Associated with <i>Z</i> <sub><i>n</i></sub>.
limited evidence
Show all credibility signals
- cautionDOI registered: No matching Crossref record was present in this response.
- cautionDOI resolves: No matching Crossref record was present in this response.
- not scoredDirectory of Open Access Journals: No matching DOAJ record was present in this response. No allow-list match; this is not evidence of low credibility.
- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: No retraction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch expression of concern: No expression of concern notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch correction: No correction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch reinstatement: No reinstatement notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- supportingOpen access status: Normalized open-access status: open.
- not scoredPublication license: Not checked or no result supplied; no credibility inference made.
- not scoredPublication version: A publication version was supplied but is not scored.
- cautionMetadata completeness: 5 of 6 scored descriptive metadata groups are present; missing fields increase uncertainty.
On the Zero Divisors and Extension of the Pythagorean Ring
limited evidence
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- cautionDOI registered: No matching Crossref record was present in this response.
- cautionDOI resolves: No matching Crossref record was present in this response.
- not scoredDirectory of Open Access Journals: No matching DOAJ record was present in this response. No allow-list match; this is not evidence of low credibility.
- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: No retraction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch expression of concern: No expression of concern notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch correction: No correction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch reinstatement: No reinstatement notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredOpen access status: Not checked or no result supplied; no credibility inference made.
- not scoredPublication license: Not checked or no result supplied; no credibility inference made.
- cautionPublication version: Identified as a preprint; peer review and later versions may change the record.
- cautionMetadata completeness: 5 of 6 scored descriptive metadata groups are present; missing fields increase uncertainty.
On Zero-Divisor Graphs of Z<em><sub>n</sub></em>, When <em>n</em> Is Square Free
limited evidence
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- cautionDOI registered: No matching Crossref record was present in this response.
- cautionDOI resolves: No matching Crossref record was present in this response.
- not scoredDirectory of Open Access Journals: No matching DOAJ record was present in this response. No allow-list match; this is not evidence of low credibility.
- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: No retraction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch expression of concern: No expression of concern notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch correction: No correction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch reinstatement: No reinstatement notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredOpen access status: Not checked or no result supplied; no credibility inference made.
- not scoredPublication license: Not checked or no result supplied; no credibility inference made.
- cautionPublication version: Identified as a preprint; peer review and later versions may change the record.
- cautionMetadata completeness: 5 of 6 scored descriptive metadata groups are present; missing fields increase uncertainty.
Zagreb Indices and Adjacency Matrices of Fuzzy Zero Divisor Graphs with MATLAB Based Algebraic Applications
limited evidence
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- cautionDOI registered: No matching Crossref record was present in this response.
- cautionDOI resolves: No matching Crossref record was present in this response.
- not scoredDirectory of Open Access Journals: No matching DOAJ record was present in this response. No allow-list match; this is not evidence of low credibility.
- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: No retraction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch expression of concern: No expression of concern notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch correction: No correction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch reinstatement: No reinstatement notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredOpen access status: Not checked or no result supplied; no credibility inference made.
- not scoredPublication license: Not checked or no result supplied; no credibility inference made.
- cautionPublication version: Identified as a preprint; peer review and later versions may change the record.
- cautionMetadata completeness: 5 of 6 scored descriptive metadata groups are present; missing fields increase uncertainty.
Zero-Divisor Graphs of ℤ_n, their products and D_n
limited evidence
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- cautionDOI registered: No matching Crossref record was present in this response.
- cautionDOI resolves: No matching Crossref record was present in this response.
- not scoredDirectory of Open Access Journals: No matching DOAJ record was present in this response. No allow-list match; this is not evidence of low credibility.
- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: No retraction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch expression of concern: No expression of concern notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch correction: No correction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch reinstatement: No reinstatement notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredOpen access status: Not checked or no result supplied; no credibility inference made.
- not scoredPublication license: Not checked or no result supplied; no credibility inference made.
- cautionPublication version: Identified as a preprint; peer review and later versions may change the record.
- cautionMetadata completeness: 5 of 6 scored descriptive metadata groups are present; missing fields increase uncertainty.
A further study of quandles and quandle rings
limited evidence
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- cautionDOI registered: No matching Crossref record was present in this response.
- cautionDOI resolves: No matching Crossref record was present in this response.
- not scoredDirectory of Open Access Journals: No matching DOAJ record was present in this response. No allow-list match; this is not evidence of low credibility.
- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: No retraction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch expression of concern: No expression of concern notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch correction: No correction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch reinstatement: No reinstatement notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- supportingOpen access status: Normalized open-access status: open.
- supportingPublication license: A publication license was supplied: https://creativecommons.org/licenses/by/4.0/legalcode. Presence improves reuse transparency, not research validity.
- cautionPublication version: Identified as a preprint; peer review and later versions may change the record.
- cautionMetadata completeness: 5 of 6 scored descriptive metadata groups are present; missing fields increase uncertainty.
Isomorphisms and automorphisms of minimal comaximal hypergraphs of commutative rings
limited evidence
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- cautionDOI registered: No matching Crossref record was present in this response.
- cautionDOI resolves: No matching Crossref record was present in this response.
- not scoredDirectory of Open Access Journals: No matching DOAJ record was present in this response. No allow-list match; this is not evidence of low credibility.
- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: No retraction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch expression of concern: No expression of concern notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch correction: No correction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch reinstatement: No reinstatement notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredOpen access status: Not checked or no result supplied; no credibility inference made.
- supportingPublication license: A publication license was supplied: http://arxiv.org/licenses/nonexclusive-distrib/1.0/. Presence improves reuse transparency, not research validity.
- cautionPublication version: Identified as a preprint; peer review and later versions may change the record.
- cautionMetadata completeness: 5 of 6 scored descriptive metadata groups are present; missing fields increase uncertainty.
The Geometric and Topological Formalization of the SHA-256 Message Schedule: Aperture Thresholds, Parity Duality, and Triadic Closure
limited evidence
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- cautionDOI registered: No matching Crossref record was present in this response.
- cautionDOI resolves: No matching Crossref record was present in this response.
- not scoredDirectory of Open Access Journals: No matching DOAJ record was present in this response. No allow-list match; this is not evidence of low credibility.
- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: No retraction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch expression of concern: No expression of concern notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch correction: No correction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch reinstatement: No reinstatement notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- supportingOpen access status: Normalized open-access status: open.
- supportingPublication license: A publication license was supplied: https://creativecommons.org/licenses/by-nc/4.0/legalcode. Presence improves reuse transparency, not research validity.
- not scoredPublication version: A publication version was supplied but is not scored.
- cautionMetadata completeness: 5 of 6 scored descriptive metadata groups are present; missing fields increase uncertainty.
AWC Conjecture J: Recursive Structure of High-Dimensional p-Modular Algebras and Projective Information Doubling
limited evidence
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- cautionDOI registered: No matching Crossref record was present in this response.
- cautionDOI resolves: No matching Crossref record was present in this response.
- not scoredDirectory of Open Access Journals: No matching DOAJ record was present in this response. No allow-list match; this is not evidence of low credibility.
- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: No retraction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch expression of concern: No expression of concern notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch correction: No correction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch reinstatement: No reinstatement notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- supportingOpen access status: Normalized open-access status: open.
- supportingPublication license: A publication license was supplied: https://creativecommons.org/licenses/by/4.0/legalcode. Presence improves reuse transparency, not research validity.
- cautionPublication version: Identified as a preprint; peer review and later versions may change the record.
- cautionMetadata completeness: 5 of 6 scored descriptive metadata groups are present; missing fields increase uncertainty.
Structural Algebras of Admissibility, Execution, and Observation in Discrete Mechanics
limited evidence
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- cautionDOI registered: No matching Crossref record was present in this response.
- cautionDOI resolves: No matching Crossref record was present in this response.
- not scoredDirectory of Open Access Journals: No matching DOAJ record was present in this response. No allow-list match; this is not evidence of low credibility.
- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: No retraction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch expression of concern: No expression of concern notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch correction: No correction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch reinstatement: No reinstatement notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- supportingOpen access status: Normalized open-access status: open.
- supportingPublication license: A publication license was supplied: https://creativecommons.org/licenses/by-nc/4.0/legalcode. Presence improves reuse transparency, not research validity.
- not scoredPublication version: A publication version was supplied but is not scored.
- cautionMetadata completeness: 5 of 6 scored descriptive metadata groups are present; missing fields increase uncertainty.
Kaplansky's conjectures fail for torsion-free hyperbolic groups in positive characteristic
limited evidence
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- cautionDOI registered: No matching Crossref record was present in this response.
- cautionDOI resolves: No matching Crossref record was present in this response.
- not scoredDirectory of Open Access Journals: No matching DOAJ record was present in this response. No allow-list match; this is not evidence of low credibility.
- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: No retraction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch expression of concern: No expression of concern notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch correction: No correction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch reinstatement: No reinstatement notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- supportingOpen access status: Normalized open-access status: open.
- supportingPublication license: A publication license was supplied: https://creativecommons.org/licenses/by/4.0/legalcode. Presence improves reuse transparency, not research validity.
- cautionPublication version: Identified as a preprint; peer review and later versions may change the record.
- cautionMetadata completeness: 5 of 6 scored descriptive metadata groups are present; missing fields increase uncertainty.
Functional edge labelings: how far a graph is from being magic
limited evidence
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- cautionDOI registered: No matching Crossref record was present in this response.
- cautionDOI resolves: No matching Crossref record was present in this response.
- not scoredDirectory of Open Access Journals: No matching DOAJ record was present in this response. No allow-list match; this is not evidence of low credibility.
- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: No retraction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch expression of concern: No expression of concern notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch correction: No correction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch reinstatement: No reinstatement notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- supportingOpen access status: Normalized open-access status: open.
- supportingPublication license: A publication license was supplied: https://creativecommons.org/licenses/by/4.0/legalcode. Presence improves reuse transparency, not research validity.
- cautionPublication version: Identified as a preprint; peer review and later versions may change the record.
- cautionMetadata completeness: 5 of 6 scored descriptive metadata groups are present; missing fields increase uncertainty.
An Interplay between Commutative Rings and Graph Theory: A Review
limited evidence
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- cautionDOI registered: No matching Crossref record was present in this response.
- cautionDOI resolves: No matching Crossref record was present in this response.
- not scoredDirectory of Open Access Journals: No matching DOAJ record was present in this response. No allow-list match; this is not evidence of low credibility.
- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: No retraction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch expression of concern: No expression of concern notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch correction: No correction notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredRetraction Watch reinstatement: No reinstatement notice matched this DOI in the deployed snapshot. No matching event found; coverage may be incomplete.
- not scoredOpen access status: Not checked or no result supplied; no credibility inference made.
- not scoredPublication license: Not checked or no result supplied; no credibility inference made.
- not scoredPublication version: A publication version was supplied but is not scored.
- supportingMetadata completeness: All 6 scored descriptive metadata groups are present.
Assessment of Distance Related Spectrum of the Zero-divisor Graph
uncertain
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- not scoredDOI registered: Not checked or no result supplied; no credibility inference made.
- not scoredDOI resolves: Not checked or no result supplied; no credibility inference made.
- not scoredDirectory of Open Access Journals: No matching DOAJ record was present in this response. No allow-list match; this is not evidence of low credibility.
- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
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- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: Not checked or no result supplied; no credibility inference made.
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- not scoredRetraction Watch reinstatement: Not checked or no result supplied; no credibility inference made.
- not scoredOpen access status: Not checked or no result supplied; no credibility inference made.
- not scoredPublication license: Not checked or no result supplied; no credibility inference made.
- not scoredPublication version: A publication version was supplied but is not scored.
- supportingMetadata completeness: All 6 scored descriptive metadata groups are present.
Automorphism of Zero Divisor Graphs of Nilradicals of Commutative Finite Local Rings
limited evidence
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- not scoredDOI registered: Not checked or no result supplied; no credibility inference made.
- not scoredDOI resolves: Not checked or no result supplied; no credibility inference made.
- not scoredDirectory of Open Access Journals: No matching DOAJ record was present in this response. No allow-list match; this is not evidence of low credibility.
- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch expression of concern: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch correction: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch reinstatement: Not checked or no result supplied; no credibility inference made.
- not scoredOpen access status: Not checked or no result supplied; no credibility inference made.
- not scoredPublication license: Not checked or no result supplied; no credibility inference made.
- not scoredPublication version: A publication version was supplied but is not scored.
- cautionMetadata completeness: 5 of 6 scored descriptive metadata groups are present; missing fields increase uncertainty.
Automorphism of Zero-Divisor Graphs of Nilradicals of Semilocal Ring \(\mathbb{Z}_pn_qn\)
limited evidence
Show all credibility signals
- not scoredDOI registered: Not checked or no result supplied; no credibility inference made.
- not scoredDOI resolves: Not checked or no result supplied; no credibility inference made.
- not scoredDirectory of Open Access Journals: No matching DOAJ record was present in this response. No allow-list match; this is not evidence of low credibility.
- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch expression of concern: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch correction: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch reinstatement: Not checked or no result supplied; no credibility inference made.
- not scoredOpen access status: Not checked or no result supplied; no credibility inference made.
- not scoredPublication license: Not checked or no result supplied; no credibility inference made.
- not scoredPublication version: A publication version was supplied but is not scored.
- cautionMetadata completeness: 5 of 6 scored descriptive metadata groups are present; missing fields increase uncertainty.
Automorphisms of Zero Divisor Graphs of Cube Radical Zero Completely Primary Finite Rings
limited evidence
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- not scoredDOI registered: Not checked or no result supplied; no credibility inference made.
- not scoredDOI resolves: Not checked or no result supplied; no credibility inference made.
- not scoredDirectory of Open Access Journals: No matching DOAJ record was present in this response. No allow-list match; this is not evidence of low credibility.
- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch expression of concern: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch correction: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch reinstatement: Not checked or no result supplied; no credibility inference made.
- not scoredOpen access status: Not checked or no result supplied; no credibility inference made.
- not scoredPublication license: Not checked or no result supplied; no credibility inference made.
- not scoredPublication version: A publication version was supplied but is not scored.
- cautionMetadata completeness: 5 of 6 scored descriptive metadata groups are present; missing fields increase uncertainty.
On the Graph-Theoretic Properties of Compressed Zero Divisor Graphs of Product Rings over \(\Pi^n_{k=1}\) \(\mathbb{Z}_{pk}\)
limited evidence
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- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch expression of concern: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch correction: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch reinstatement: Not checked or no result supplied; no credibility inference made.
- not scoredOpen access status: Not checked or no result supplied; no credibility inference made.
- not scoredPublication license: Not checked or no result supplied; no credibility inference made.
- not scoredPublication version: A publication version was supplied but is not scored.
- cautionMetadata completeness: 5 of 6 scored descriptive metadata groups are present; missing fields increase uncertainty.
Some Aspects of Zero-divisor Graph of \(\Gamma(\mathbb{Z}_{p}\times\mathbb{Z}_{p}), \Gamma(\mathbb{Z}_{p}^{m})\)
limited evidence
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- not scoredDirectory of Open Access Journals: No matching DOAJ record was present in this response. No allow-list match; this is not evidence of low credibility.
- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch expression of concern: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch correction: Not checked or no result supplied; no credibility inference made.
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- not scoredOpen access status: Not checked or no result supplied; no credibility inference made.
- not scoredPublication license: Not checked or no result supplied; no credibility inference made.
- not scoredPublication version: A publication version was supplied but is not scored.
- cautionMetadata completeness: 5 of 6 scored descriptive metadata groups are present; missing fields increase uncertainty.
Spectral Analysis of Compressed Zero Divisor Graphs Over \(\Pi^n_{k_=1}\) \(\mathbb{Z}_{pk}\) for 2 ≤ n ≤ 5, Where Each pk is a Prime
limited evidence
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- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch expression of concern: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch correction: Not checked or no result supplied; no credibility inference made.
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- not scoredOpen access status: Not checked or no result supplied; no credibility inference made.
- not scoredPublication license: Not checked or no result supplied; no credibility inference made.
- not scoredPublication version: A publication version was supplied but is not scored.
- cautionMetadata completeness: 5 of 6 scored descriptive metadata groups are present; missing fields increase uncertainty.
Structural Properties of Zero-Divisor Graphs of Multilocal Finite Rings
limited evidence
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- not scoredDirectory of Open Access Journals: No matching DOAJ record was present in this response. No allow-list match; this is not evidence of low credibility.
- not scoredMEDLINE indexed: Not checked or no result supplied; no credibility inference made.
- not scoredOpenAlex core source: Not checked or no result supplied; no credibility inference made.
- not scoredKnown publisher allow-list: Not checked or no result supplied; no credibility inference made.
- not scoredROR affiliation: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch retraction: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch expression of concern: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch correction: Not checked or no result supplied; no credibility inference made.
- not scoredRetraction Watch reinstatement: Not checked or no result supplied; no credibility inference made.
- not scoredOpen access status: Not checked or no result supplied; no credibility inference made.
- not scoredPublication license: Not checked or no result supplied; no credibility inference made.
- not scoredPublication version: A publication version was supplied but is not scored.
- cautionMetadata completeness: 5 of 6 scored descriptive metadata groups are present; missing fields increase uncertainty.