Commuting graphs and semigroup constructions

TL;DR

This paper explores how commuting graphs of semigroups are affected by zero-union and direct product constructions, analyzing properties like diameter, clique number, girth, chromatic number, and knit degree.

Contribution

It provides a detailed investigation of the interaction between semigroup constructions and their commuting graph properties, revealing relationships and differences.

Findings

Commuting graph properties are influenced by semigroup constructions.

Relationships between properties of original and constructed semigroups' commuting graphs.

Insights into how algebraic operations affect graph-theoretic characteristics.

Abstract

The aim of this paper is to see how commuting graphs interact with two semigroup constructions: the zero-union and the direct product. For both semigroup constructions, we investigate the diameter, clique number, girth, chromatic number and knit degree of their commuting graphs and, when possible, we exhibit the relationship between each one of these properties and the corresponding properties of the commuting graphs of the original semigroups.