- Turkish Journal of Mathematics and Computer Science
- Vol: 14 Issue: 2
- On the Essential Element Graph of a Lattice
On the Essential Element Graph of a Lattice
Authors : Alper ÜLKER
Pages : 248-255
Doi:10.47000/tjmcs.885881
View : 6 | Download : 2
Publication Date : 2022-12-30
Article Type : Research
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