Vertex and Edge connectivity of the zero divisor graph $\Gamma [{\mathbb{Z}}_n]$

Abstract

The Zero divisor Graph of a commutative ring $R$, denoted by $\Gamma [R]$, is a graph whose vertices are non-zero zero divisors of $R$ and two vertices are adjacent if their product is zero. In this paper we derive the Vertex and Edge Connectivity of the zero divisor graph $\Gamma [{\mathbb{Z}}_n]$, for any natural number $n$ . We also discuss the minimum degree of the zero divisor graph $\Gamma [{\mathbb{Z}}_n]$.

7 pages