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Keywords:
annihilating-ideal graph; lattice; line graph; planar graph; projective graph
Summary:
Let $(L,\wedge ,\vee )$ be a finite lattice with a least element 0. $\mathbb {A} G(L)$ 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 $I \wedge J=0$. We completely characterize all finite lattices $L$ whose line graph associated to an annihilating-ideal graph, denoted by $\mathfrak {L}(\mathbb {A} G(L))$, is a planar or projective graph.
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