New Families of tripartite graphs with local antimagic chromatic number 3

TL;DR

This paper introduces new families of tripartite graphs constructed via matrix methods that have a local antimagic chromatic number of 3, expanding understanding of graph labelings.

Contribution

It presents novel constructions of tripartite graphs with a local antimagic chromatic number of 3 using matrix-based methods, providing infinitely many examples.

Findings

Constructed several infinite families of tripartite graphs with chromatic number 3.

Demonstrated the use of fixed-size matrices in graph labeling constructions.

Enhanced the catalog of graphs with known local antimagic chromatic properties.

Abstract

For a graph $G(V,E)$ of size $q$, a bijection $f : E(G) \to [1,q]$ is a local antimagc labeling if it induces a vertex labeling $f^+ : V(G) \to \mathbb{N}$ such that $f^+(u) \ne f^+(v)$, where $f^+(u)$ is the sum of all the incident edge label(s) of $u$, for every edge $uv \in E(G)$. In this paper, we make use of matrices of fixed sizes to construct several families of infinitely many tripartite graphs with local antimagic chromatic number 3.