On local antimagic chromatic number of the join of two special families of graphs -- II

TL;DR

This paper investigates the local antimagic chromatic number of graph joins, proving that joining a 1-regular graph with a null graph results in a chromatic number of 3, and identifies various bipartite and tripartite graphs with this property.

Contribution

It establishes new results on the local antimagic chromatic number for joins of specific graph families, expanding understanding of graph coloring properties.

Findings

Join of 1-regular and null graphs has local antimagic chromatic number 3

Identifies multiple bipartite and tripartite graphs with chromatic number 3

Provides new classes of graphs with known local antimagic chromatic number

Abstract

It is known that null graphs and 1-regular graphs are the only regular graphs without local antimagic chromatic number. In this paper, we proved that the join of 1-regular graph and a null graph has local antimagic chromatic number is 3. Consequently, we also obtained many families of (possibly disconnected or regular) bipartite and tripartite graph with local antimagic chromatic number 3.