Some results on a supergraph of the sum annihilating ideal graph of a commutative ring

The rings considered in this paper are commutative with identity which are not integral domains. Let R be a ring. An ideal I of R is said to be an annihilating ideal if there exists r is an element of R\{0} such that Ir = (0). Let A(R) denote the set of all annihilating ideals of R and we denote A(R)\{(0)} by A(R)*. With R, in this paper, we associate an undirected graph denoted by S Omega(R) whose vertex set is A(R)* and two distinct vertices I, J are adjacent in this graph if and only if either IJ = (0) or I + J is an element of A(R). The aim of this paper is to study the interplay between some graph properties of S Omega(R) and the algebraic properties of R and to compare some graph properties of S Omega(R) with the corresponding graph properties of the annihilating ideal graph of R and the sum annihilating ideal graph of R.