Zero divisor graph of boolean lattice

Abstract

The concept of zero divisor graph has been previously studied in algebraic structures like commutative rings, semi groups, semi lattices and ordered sets. In this paper, we investigate the properties of zero divisor graph of boolean lattices. Let L be a lattice and Γ(L) be the zero divisor graph of L. We find a relationship between the clique number and chromatic number of Γ(L) and some properties of zero divisor graph of boolean lattices. We also study the relationship between aut(L) and aut(Γ(L)) and establish the isomorphism between them.