On local antimagic chromatic number of various join graphs

A local antimagic edge labeling of a graph G = (V, E) is a bijection f : E → {1, 2, . . . , |E|} such that the induced vertex labeling f + : V → Z given by f +(u) = ∑f(e), where the summation runs over all edges e incident to u, has the property that any two adjacent vertices have distinct labels. A graph G is said to be locally antimagic if it admits a local antimagic edge labeling. The local antimagic chromatic number χla(G) is the minimum number of distinct induced vertex labels over all local antimagic labelings of G. In this paper we obtain sufficient conditions under which χla(G ∨ H), where H is either a cycle or the empty graph On = Kn, satisfies a sharp upper bound. Using this we determine the value of χla(G ∨ H) for many wheel related graphs G.