On the Essential Element Graph of a Lattice

Abstract

Let mathcalL be a bounded lattice. The essential element graph of mathcalL is a simple undirected graph varepsilonmathcalL such that the elements x,y of mathcalL form an edge in varepsilonmathcalL, whenever xveey is an essential element of mathcalL. 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.