Geodesic
When a line graph associated to annihilating-ideal graph of a lattice is planar or projective
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 1, pp. 19-34 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/CMJ.2018.0635-15
Classification : 05C10, 05C75, 06B10
Keywords: annihilating-ideal graph; lattice; line graph; planar graph; projective graph 
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Parsapour, Atossa; Ahmad Javaheri, Khadijeh. When a line graph associated to annihilating-ideal graph of a lattice is planar or projective. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 1, pp. 19-34. doi: 10.21136/CMJ.2018.0635-15

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