On Local Antimagic Chromatic Number of Cycle-Related Join Graphs

An edge labeling of a connected graph G = (V, E) is said to be local antimagic if it is a bijection f: E → {1, |E|} such that for any pair of adjacent vertices x and y, f+(x) f+(y), where the induced vertex label f+(x) = ςf(e), with e ranging over all the edges incident to x. The local antimagic chromatic number of G, denoted by χla(G), is the minimum number of distinct induced vertex labels over all local antimagic labelings of G. In this paper, several sufficient conditions for χla(H) ≤ χla(G) are obtained, where H is obtained from G with a certain edge deleted or added. We then determined the exact value of the local antimagic chromatic number of many cycle-related join graphs.