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

Parsapour, Atossa; Javaheri, Khadijeh Ahmad

doi:10.21136/cmj.2018.0635-15

Cited by 3 publications

(2 citation statements)

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“…The planar and crosscap one annihilating-ideal graph of lattices were characterized by Shahsavar [19] and Parsapour et al [20], respectively. Additionally, whether the line graph associated with the annihilating-ideal graph of a lattice is planar or projective was characterized by Parsapour et al [21]. Moreover, the authors of [22] characterized all lattices L whose line graph of AG(L) is toroidal.…”

Section: Introductionmentioning

confidence: 99%

“…Additionally, whether the line graph associated with the annihilating-ideal graph of a lattice is planar or projective was characterized by Parsapour et al [21]. Moreover, the authors of [22] characterized all lattices L whose line graph of AG(L) is toroidal. Now, this paper aims to classify lattices with a number of atoms less than or equal to four whose annihilating-ideal graph can be embedded in the non-orientable surfaces of crosscap two.…”

Section: Introductionmentioning

confidence: 99%

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Class of Crosscap Two Graphs Arising from Lattices–I

et al. 2023

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Let L be a lattice. The annihilating-ideal graph of L is a simple graph whose vertex set is the set of all nontrivial ideals of L and whose two distinct vertices I and J are adjacent if and only if I∧J=0. In this paper, crosscap two annihilating-ideal graphs of lattices with at most four atoms are characterized. These characterizations provide the classes of multipartite graphs, which are embedded in the Klein bottle.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Class of Crosscap Two Graphs Arising from Lattices–I

et al. 2023

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Strong metric dimension in annihilating-ideal graph of commutative rings

Jalali

Nikandish

2022

AAECC

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Class of crosscap two graphs arising from lattices-Ⅱ

Al-Bar,

Asir,

Mano

et al. 2023

MATH

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<abstract><p>In this series of papers, we study the crosscap two embedding of a class of multipartite graphs, namely, annihilating-ideal graphs of a lattice. In Part 1 of the series [Class of crosscap two graphs arising from lattices-Ⅰ, <italic>Mathematics</italic>, <bold>11</bold> (2023), 1-26], we classified lattices with the number of atoms less than or equal to 4, whose annihilating-ideal graph can be embedded in the Klein bottle. In this paper, which is Part 2 of the series, we classify all finite lattices with at least 5 atoms whose annihilating-ideal graph is embedded in crosscap two surfaces. These characterizations help us to identify classes of multipartite graphs, which are embedded in the Klein bottle.</p></abstract>

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

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Cited by 3 publications

References 16 publications

Class of Crosscap Two Graphs Arising from Lattices–I

Class of Crosscap Two Graphs Arising from Lattices–I

Strong metric dimension in annihilating-ideal graph of commutative rings

Class of crosscap two graphs arising from lattices-Ⅱ

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