Lattice automorphism and zero‐divisor graphs of lattices

Abstract

Let  be a bounded lattice and 𝛼 :  →  be its automorphism. In this paper, we study zero-divisor graph of  with respect to an automorphism 𝛼. It is a simple undirected graph and denoted by Γ 𝛼 (). Some combinatorial structures such as coloring, diameter and girth were given for Γ 𝛼 ().