On the harmonious chromatic number of graphs

TL;DR

This paper investigates the harmonious chromatic number of graphs, providing new results related to graph homomorphisms, incidence graphs of finite linear systems, and circulant graphs.

Contribution

It offers novel bounds and properties of the harmonious chromatic number in specific classes of graphs, expanding understanding of graph colorings.

Findings

Results on harmonious chromatic number related to homomorphisms

Analysis of incidence graphs of finite linear systems

Properties of harmonious chromatic number in circulant graphs

Abstract

The harmonious chromatic number of a graph $G$ is the minimum number of colors that can be assigned to the vertices of $G$ in a proper way such that any two distinct edges have different color pairs. This paper gives various results on harmonious chromatic number related to homomorphisms, incidence graphs of finite linear systems, and some circulant graphs.