A generalization of zero-divisor graphs

TL;DR

This paper introduces a new family of graphs extending zero-divisor graphs, analyzes their structural properties including diameter, cycles, and cores, and provides bounds and insights into their topology.

Contribution

It generalizes zero-divisor graphs and explores their properties, including diameter bounds, cycles, and cores, offering new insights into their structure.

Findings

Computed an upper bound for the diameter of the generalized graphs

Analyzed the cycles and cores of these graphs

Provided structural insights into the topology of the generalized graphs

Abstract

In this paper, we introduce a family of graphs which is a generalization of zero-divisor graphs and compute an upper-bound for the diameter of such graphs. We also investigate their cycles and cores.