The annihilating-ideal graph of z(n) is weakly perfect

Nikandish, Reza, Maimani, Hamid Reza and Izanloo, Hassan 2016. The annihilating-ideal graph of z(n) is weakly perfect. Contributions to Discrete Mathematics 11 (1) , pp. 16-21. 10.11575/cdm.v11i1.62406

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Abstract

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

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	University of Calgary
ISSN:	1715-0868
Date of First Compliant Deposit:	14 December 2018
Last Modified:	04 May 2023 22:24
URI:	https://orca.cardiff.ac.uk/id/eprint/117592

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