A note on unitary Cayley graphs of matrix algebras

Yihan Chen; Bicheng Zhang

A note on unitary Cayley graphs of matrix algebras

Combinatorics 2020-06-17 v3 Rings and Algebras

Authors: Yihan Chen , Bicheng Zhang

Abstract

Dariush Kiani et al.\cite{kiani2015unitary} claim to have found the unitary Cayley graph $Cay(M_{n}(F),GL_{n}(F))$ of matrix algebras over finite field $F$ is strongly regular only when $n=2$ , but they have only considered two special cases, namely when $n = 2$ and $3$ and have failed to cover the general cases. In this paper, we prove that the unitary Cayley graph of matrix algebras over finite field $F$ is strongly regular if and only if $n=2$ .

Keywords

unitary cayley graph matrix algebra finite field strongly regular graph general linear group

Cite

@article{arxiv.1904.11868,
  title  = {A note on unitary Cayley graphs of matrix algebras},
  author = {Yihan Chen and Bicheng Zhang},
  journal= {arXiv preprint arXiv:1904.11868},
  year   = {2020}
}

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