Local edge antimagic chromatic number of join product of graphs

Maryati, Tita Khalis (UIN Syarif Hidayatullah Jakarta)
Hadiputra, Fawwaz Fakhrurrozi (The University of Melbourne)

Indonesian Journal of Combinatorics
Vol 9, No 2 (2025)

Let f : V(G) \to [1,|V(G)|] be a bijective mapping of the vertex set of a graph G to the integers 1 through |V(G)|. A labeling f is defined as a local edge antimagic labeling if, for any two adjacent edges uv and vx in E(G), their weights satisfy wf(uv) ≠ wf(vx), where the weight of an edge uv is given by wf(uv) = f(u) + f(v). The weight wf induces a proper edge coloring on G. The local edge antimagic chromatic number of G, denoted χlea'(G), is the minimum number of colors required among all colorings induced by local edge antimagic labelings of G. In this paper, we investigate the local edge antimagic coloring of join product of graphs, particularly for independent sets, paths, and cycles.