Some Properties of the Zero-Divisor Graphs of Idealization Ring R(+)M

Abstract

The aim of this article to follow the properties of the zero-divisor graph of special idealization ring. We study the wiener index of the zero-divisors graph of some special idealization ring R(+)M and find the clique number of the graph Γ(R(+)M) is ω (Γ(R(+)M)) = |M| − 1, where R is an integral domain. We also discuss when the zero-divisors graph of some special idealization ring R(+)M are Hamiltonian graph.