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PreprintarXiv licencearXiv

Finite Matrix Rings of Even Size Are Determined by Their Commuting Graphs

  • Hamid Shahverdi
  • Vahid Shahverdi
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Abstract

The commuting graph of a noncommutative ring has its noncentral elements as vertices, with two distinct vertices adjacent when they commute. Akbari, Ghandehari, Hadian and Mohammadian conjectured that a full matrix ring over a finite field is determined, among rings with identity, by its commuting graph. In this paper, we prove the conjecture for every even matrix size.

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Cite

BibTeXRIS
BibTeX
@misc{shahverdi2026finite,
  title = {{Finite Matrix Rings of Even Size Are Determined by Their Commuting Graphs}},
  author = {Hamid Shahverdi and Vahid Shahverdi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37150},
  eprint = {2610.37150},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37150},
}
RIS
TY  - UNPB
TI  - Finite Matrix Rings of Even Size Are Determined by Their Commuting Graphs
AU  - Hamid Shahverdi
AU  - Vahid Shahverdi
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37150
UR  - https://arxiv.org/abs/2610.37150
AB  - The commuting graph of a noncommutative ring has its noncentral elements as vertices, with two distinct vertices adjacent when they commute. Akbari, Ghandehari, Hadian and Mohammadian conjectured that a full matrix ring over a finite field is determined, among rings with identity, by its commuting graph. In this paper, we prove the conjecture for every even matrix size.
ER  -