On the Structure of Nil Graph of a Commutative Ring

Authors

  • Kuntala Patra Gauhati University
  • Shazida Begum Gauhati University

DOI:

https://doi.org/10.11113/matematika.v31.n1.629

Abstract

Let R be a commutative ring and N(R) be the set of all non-zero nil elements of index two. The Nil Graph of R, denoted by Γ_N(R), is an undirected graph with the vertex set ZN(R)*={x ϵ R*| xy ϵ N(R) for some y in R*=R-{0}} and any two vertices of ZN(R)* are adjacent if and only if xy ϵ N(R). In this paper we determine the chromatic number of the nil graph Γ_N (Z_(p^\alpha q)) . Also we study the diameter and girth of Γ_N (Z_(p^\alpha q)).

Downloads

Published

2015-07-28

Issue

Section

Articles