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

Atossa Parsapour; Khadijeh Ahmad Javaheri

Czechoslovak Mathematical Journal (2018)

  • Volume: 68, Issue: 1, page 19-34
  • ISSN: 0011-4642

Abstract

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Let ( L , ∧ , ∨ ) be a finite lattice with a least element 0. 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 ∧ J = 0 . We completely characterize all finite lattices L whose line graph associated to an annihilating-ideal graph, denoted by 𝔏 ( 𝔸 G ( L ) ) , is a planar or projective graph.

How to cite

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Parsapour, Atossa, and Ahmad Javaheri, Khadijeh. "When a line graph associated to annihilating-ideal graph of a lattice is planar or projective." Czechoslovak Mathematical Journal 68.1 (2018): 19-34. <http://eudml.org/doc/294241>.

@article{Parsapour2018,
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.},
author = {Parsapour, Atossa, Ahmad Javaheri, Khadijeh},
journal = {Czechoslovak Mathematical Journal},
keywords = {annihilating-ideal graph; lattice; line graph; planar graph; projective graph},
language = {eng},
number = {1},
pages = {19-34},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {When a line graph associated to annihilating-ideal graph of a lattice is planar or projective},
url = {http://eudml.org/doc/294241},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Parsapour, Atossa
AU - Ahmad Javaheri, Khadijeh
TI - When a line graph associated to annihilating-ideal graph of a lattice is planar or projective
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 1
SP - 19
EP - 34
AB - 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.
LA - eng
KW - annihilating-ideal graph; lattice; line graph; planar graph; projective graph
UR - http://eudml.org/doc/294241
ER -

References

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