When a line graph associated to annihilating-ideal graph of a lattice is planar or projective

Czechoslovak Mathematical Journal

Atossa Parsapour, Khadijeh Ahmad Javaheri¹ 

关键词: annihilating-ideal graph;    lattice;    line graph;    planar graph;    projective graph;   

DOI  :  10.21136/CMJ.2018.0635-15

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

  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.

【 授权许可】

Unknown