Generators of the automorphism group of a regular graph over a ring

Abstract

Let R be a ring with unity, Z(R) the subset of R of all zero-divisors in R, Reg the set of all regular elements of R. The regular graph of R, denoted by Reg, is a graph with Reg(R) as vertex set, and two distinct vertices Reg(R) are adjacent if and only if . If is the ring of all upper triangular matrices over a finite field F, then Z(R) consists of singular matrices in R and Reg(R) consists of nonsingular matrices in R. In this paper, the automorphisms of Reg with F a finite field are determined.

Keywords:

• Total graph
• regular graph
• automorphisms

AMS Subject Classifications:

• 05C35
• 05C50
• 15A15
• 20H20

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11571360].