Abstract
Let (L,โง, โจ) be a finite lattice with a least element 0. AG(L) is an annihilating-ideal graph of L in which the vertex set is the set of all nontrivial ideals of L, and two distinct vertices I and J are adjacent if and only if I โง J = 0. We completely characterize all finite lattices L whose line graph associated to an annihilating-ideal graph, denoted by L(AG(L)), is a planar or projective graph.
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