On automorphism group of orthogonality graph of finite semisimple rings

Abstract

The orthogonality graph of a ring R, written as O(R), is an undirected simple graph with vertex set $Z^{\#}(R),$ the set of all nonzero two-sides zero-divisors of R, and for distinct $x,y\in Z^{\#}(R)$ there exists an edge joining x and y if and only if $xy=yx=0.$ In this paper, we describe the automorphism group of O(R) when R is a finite semisimple ring.

Keywords:

• Automorphism groups
• orthogonality graphs

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 05C25
• 15A86
• 20D45

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (No. 11971474, 11661040), and the Foundation of Education Department of Jiangxi Province (No. GJJ200838).