Lattices, whose incomparability graphs have horns

Wasadikar, Meenakshi; Survase, Pradnya

doi:10.1016/j.jda.2013.07.001

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Coloring Connectedness and Girth1

Introduction1

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Cited by 2 publications

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“…This graph is denoted by IC(ℒ). Incomparability graphs of lattices are studied in [27]. Theorem Let ℒ be a bounded lattice and α : ℒ → ℒ be an automorphism.…”

Section: Coloring Connectedness and Girthmentioning

confidence: 99%

“…Total graphs of lattices was introduced and studied extensively in [6]. The graphs associated to lattices such as incomparability graphs [27], crown‐free lattices graphs studied by authors in [8]. In [25], Patil, Khairnar, and Waphare studied zero‐divisor graph of a poset with respect to an automorphism and they introduced generalized zero‐divisor graph of a partially ordered set.…”

Section: Introductionmentioning

confidence: 99%

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Lattice automorphism and zero‐divisor graphs of lattices

Ülker

2021

Numerical Methods Partial

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“…This graph is denoted by IC(ℒ). Incomparability graphs of lattices are studied in [27]. Theorem Let ℒ be a bounded lattice and α : ℒ → ℒ be an automorphism.…”

Section: Coloring Connectedness and Girthmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Lattice automorphism and zero‐divisor graphs of lattices

Ülker

2021

Numerical Methods Partial

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On the Essential Element Graph of a Lattice

Ülker

2022

Turkish Journal of Mathematics and Computer Science

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Let $\mathcal{L}$ be a bounded lattice. The essential element graph of $\mathcal{L}$ is a simple undirected graph $\varepsilon_{\mathcal{L}}$ such that the elements $x,y$ of $\mathcal{L}$ form an edge in $\varepsilon_{\mathcal{L}}$, whenever $x \vee y $ is an essential element of $\mathcal{L}$. In this paper, we study properties of the essential elements of lattices and essential element graphs. We study the lattices whose zero-divisor graphs and incomparability graphs are isomorphic to its essential element graphs. Moreover, the line essential element graphs are investigated.

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Lattices, whose incomparability graphs have horns

Cited by 2 publications

References 4 publications

Lattice automorphism and zero‐divisor graphs of lattices

Lattice automorphism and zero‐divisor graphs of lattices

On the Essential Element Graph of a Lattice

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