Cut edges and Central vertices of zero divisor graph of the ring of integers modulo n

TL;DR

This paper investigates the structural properties of the zero divisor graph of the ring of integers modulo n, focusing on identifying cut-edges and central vertices.

Contribution

It provides a characterization of cut-edges and central vertices specifically for the zero divisor graph of rac{rac{rac{{Z}_{n}}{}}{}}.

Findings

Identifies all cut-edges in rac{rac{rac{{Z}_{n}}{}}{}}.

Determines the central vertices in the zero divisor graph of rac{rac{rac{{Z}_{n}}{}}{}}.

Abstract

The zero divisor graph of a commutative ring $R$ with unity is a graph whose vertices are the nonzero zero-divisors of the ring, with two distinct vertices being adjacent if their product is zero. This graph is denoted by $\Gamma(R)$. In this article we determine the cut-edges and central vertices in the graph $\Gamma(\mathbb{Z}_{n})$.