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.

arXiv admin note: text overlap with arXiv:2408.04942