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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Silaban, Denny Riama
Departments of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok - Indonesia
Electrical & Electronics Engineering

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Local edge antimagic chromatic number of comb products involving path graph Chandra, Ivana Joice; Silaban, Denny Riama
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 13, No 1 (2025): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2025.13.1.12

Abstract

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.
Co-Authors Chandra, Ivana Joice