New Families of tripartite graphs with local antimagic chromatic number 3

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.