On join product and local antimagic chromatic number of regular graphs

Let $$G = (V,E)$$ be a connected simple graph of order p and size q. A G is called local antimagic if admits labeling. bijection $$f \colon E \to \{1,2,\ldots,q\}$$ labeling for any two adjacent vertices $$u$$ $$v$$ , we have $$f^+(u) \ne f^+(v)$$ where \sum_{e\in E(u)} f(e)$$ $$E(u)$$ the set edges incident to . Thus, induces proper vertex coloring assigned color $$f^+(v)$$ The chromatic number, denoted $$\chi_{la}(G)$$ minimum number induced colors taken over G. H disjoint graphs. join H, \vee H$$ with $$V(G\vee H) V(G) \cup V(H)$$ $$E(G\vee E(G) E(H) \{uv \mid u\in V(G)$$ $$v \in V(H)\}$$ In this paper, investigated $$\chi_{la}(G\vee H)$$ Consequently, show existence non-complete regular graphs arbitrarily large order, regularity numbers.