On the Essential Element Graph of a Lattice

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Turkish Journal of Mathematics and Computer Science
Volume:14 Issue:2
On the Essential Element Graph of a Lattice

On the Essential Element Graph of a Lattice

Pages : 248-255

View : 22 | Download : 14

Publication Date : 2022-12-30

Article Type : Research Paper

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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