On local antimagic chromatic numbers of the join of two special families of graphs

It is known that null graphs are the only (regular) graphs with local antimagic chromatic 1 and 1-regular graphs are the only regular graphs without local antimagic chromatic number. In this paper, we first use matrices of size \((2m+1) × (2k+1)\) to completely determine the local antimagic chromatic number of the join of null graphs \(O_m\) and 1-regular graphs \((2k+1)P_2\) for all \(k≥ 1, m≥ 2\). We then make use of other matrices of same size to obtain the local antimagic chromatic number of another family of tripartite graphs. Consequently, we obtained infinitely many (possibly disconnected) regular tripartite graphs with local antimagic chromatic number 3.