# Article

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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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