On Connectivity of Zero-Divisor Graphs and Complement Graphs of some Semi-Local Rings

Abstract

Zero-divisor graphs have been a key area of focus for many researchers. For the semi local ring R of finite cartesian product of finite fields, we consider the zero divisor graph of R denoted by Γ(R) with vertex set as the non-zero zero-divisors of R where two vertices u and v are adjacent if and only if the product of u and v is the additive identity of the Ring R. The objective of this paper is to determine the number of cut vertices and cut edges, vertex connectivity and edge connectivity of the zero divisor graph Γ(R) and complement graph Γ(R).