The annihilating-ideal graph of Zn is weakly perfect

Authors

  • Reza Nikandish Department of Mathematics, Jundi-Shapur University of Technology
  • Hamidreza Maimani Rajaee Teacher Training University
  • Hasan Izanloo Cardiff University

DOI:

https://doi.org/10.11575/cdm.v11i1.62406

Abstract

A graph is called weakly perfect if its vertex chromatic number equals its clique number. Let R be a commutative ring with identity and A(R) be the set of ideals with non-zero annihilator. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A(R)=A(R){0} and two distinct vertices I and J are adjacent if and only if IJ=0. In this paper, we show that the graph AG(Zn), for every positive integer n, is weakly perfect. Moreover, the exact value of the clique number of AG(Zn) is given and it is proved that AG(Zn) is class 1 for every positive integer n.

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Published

2016-07-19

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Section

Articles