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Abstract
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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.
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