On Sum Element Ideal Graphs

Abstract

Let R be a commutative ring with identity and let x be an element of R. The element ideal graph is a graph whose vertex set is the set of non-trivial ideals of R and two distinct vertices I and J are adjacent if and only if xIJ. In this paper, we consider a new kind of graph associated with R denoted by whose vertex set is the set of non-trivial ideals of R and two distinct vertices I and J are adjacent if and only if I+J is a vertex of .