Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 68, No. 1, pp. 19-34, 2018

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

Atossa Parsapour, Khadijeh Ahmad Javaheri

Received November 25, 2015. First published January 11, 2018.

Abstract: 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.

Keywords: annihilating-ideal graph; lattice; line graph; planar graph; projective graph

Classification MSC: 05C75, 05C10, 06B10

DOI: 10.21136/CMJ.2018.0635-15

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Atossa Parsapour (corresponding author), Khadijeh Ahmad Javaheri, Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, P. O. Box 79159-1311, Bandar Abbas 7915893144, Iran, e-mail: a.parsapour2000@yahoo.com, javaheri1158kh@yahoo.com

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