Local edge antimagic chromatic number of comb products involving path graph - Chandra, Ivana Joice; Silaban, Denny Riama (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2025)
Let G = (V, E) be a graph with n vertices and no isolated vertices. A local edge antimagic labeling of G is a bijection f : V(G)→1, 2, …, n such that the weights of any two adjacent edges in G are distinct, where the weight of an edge in G is defined as the sum of the labels of its end vertices. Such a labeling induces a proper edge coloring of G, with edge weights serving as the colors. The local edge antimagic chromatic number of G, denoted χ′lea(G), is the minimum number of colors used across all such labelings. In this paper, we investigate the local edge antimagic chromatic number of comb product graphs, focusing on the case where a path graph is combined with copies of other graphs—specifically paths, cycles, and ladders. The comb product of G and H, with respect to an assigned vertex, is constructed by taking one copy of G and |V(G)| copies of H and identifying the assigned vertex from the i-th copy of H to the i-th vertex of G.