### The Element ideal graph Γ(pα qβ ) (Z)

Department of Mathematics, College of Education, Salahaddin University – Hawler, Iraq

DOI: https://doi.org/10.17656/jzs.10547

Abstract

Let R be acommutative ring with identity and let x be an element of R. The Element Ideal Graph Γx (R) is a graph whose vertex set is the set of non-trivial ideals of R and two distinct ideal vertices I and J are adjacent if and only if x∈I J. In this paper we investigate the element ideal graph Γ(pα qβ ) (Z) to explore some of its properties with providing some examples, where Z is the set of integers, α, β∈Z+    and p and q are distinct prime numbers.

Key Words:  Element Ideal Graph, Clique , Diameter.

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