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

TL;DR

This paper investigates the vertex and edge connectivity of the zero divisor graph of the ring of integers modulo n, providing formulas and properties for these graph invariants.

Contribution

It derives the vertex and edge connectivity of zero divisor graphs for all natural numbers n, a novel contribution to algebraic graph theory.

Findings

Vertex connectivity formulas for $ abla[ ext{Z}_n]$

Edge connectivity formulas for $ abla[ ext{Z}_n]$

Analysis of the minimum degree of the graph

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 $\Gamma[\mathbb{Z}_n]$.