On the Essential Element Graph of a Lattice

Year 2022, Volume: 14 Issue: 2, 248 - 255, 30.12.2022

Alper Ülker

https://doi.org/10.47000/tjmcs.885881

Abstract

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.

Keywords

Lattice, zero-divisor graph, essential element, annihilator

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