A new graph associated to a commutative ring

Let R be a commutative ring with identity which is not an integral domain . An ideal I of a ring R is called an annihilating ideal if there exists r R {0}such that Ir (0) . In this note, we investigate the domination number of a new simple undirected graph associated with R denoted by (R)whose vertex set,  , equals the set of all nonzero annihilating ideals of R , and two distinct vertices I , J in this graph are joined by an edge if and only if I+J is also an annihilating ideal of R.

Keywords:

Commutative rings , annihilation ideal , graph