Zero-divisor graphs of lower dismantlable lattices-I

TL;DR

This paper explores the structure of zero-divisor graphs within a specific subclass of dismantlable lattices, linking their properties to non-ancestor graphs of rooted trees for better understanding.

Contribution

It introduces a characterization of zero-divisor graphs of lower dismantlable lattices using non-ancestor graphs, providing new insights into their structure.

Findings

Zero-divisor graphs are characterized by non-ancestor graphs of rooted trees.

A new connection between lattice theory and graph theory is established.

The study advances understanding of dismantlable lattices' algebraic and combinatorial properties.

Abstract

In this paper, we study the zero-divisor graphs of a subclass of dismantlable lattices. These graphs are characterized in terms of the non-ancestor graphs of rooted trees.