Sum ideal graphs associated to a given ideal of a commutative ring

Abstract EN

The aim of this paper is to introduce and study a new kind of graphs associated to an ideal of a commutative ring.

Let ℛ be a commutative ring with identity, and I(ℛ) be the set of all non-trivial ideals of ℛ with S I(ℛ).

The sum ideal graph associated to S, denoted by Ψ(ℛ, S), is the undirected graph with vertex set {A I(ℛ): S⊂A+B, for some B I(ℛ)} where two ideal vertices A and B are adjacent if and only if A B and S⊂A+B.

In this paper we establish some of characterizations and results of this kind of graph with providing some examples.