the sum-annihilating essential ideal graph of a commutative ring

let $r$ be a commutative ring with identity. an ideal $i$ of a ring $r$is called an annihilating ideal if there exists $rin rsetminus {0}$ such that $ir=(0)$ and an ideal $i$ of$r$ is called an essential ideal if $i$ has non-zero intersectionwith every other non-zero ideal of $r$. thesum-annihilating essential ideal graph of $r$, denoted by $mathcal{ae}_r$, isa graph whose vertex set is the set of all non-zero annihilating ideals and twovertices $i$ and $j$ are adjacent whenever ${rm ann}(i)+{rmann}(j)$ is an essential ideal. in this paper we initiate thestudy of the sum-annihilating essential ideal graph. we first characterize all rings whose sum-annihilating essential ideal graph are stars or complete graphs and then establish sharp bounds on domination number of this graph. furthermore determine all isomorphism classes of artinian rings whose sum-annihilating essential ideal graph has genus zero or one.