مشخصات پژوهش

Let R be a commutative ring with identity which is not an inte- gral domain. An ideal I of R is called an annihilating ideal if there exists r 2 R n f0g such that Ir = (0). The sum- annihilating ideal graph is a simple undirected graph (R), as- sociated with R, as follows: the vertex set of (R) is the set of all non-zero annihilating ideals of R, and two distinct vertices I, J are adjacent if and only if I+J is also an annihilating ideal of R. In this paper we rst establish sharp bounds on domination number of the sum-annihilating ideal graph and then we char- acterize all commutative rings R whose the sum-annihilating ideal graph (R) have genus zero or one.