Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 13, No 1 (2025): Electronic Journal of Graph Theory and Applications

Local edge antimagic chromatic number of comb products involving path graph

Chandra, Ivana Joice (Departments of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok - Indonesia)
Silaban, Denny Riama (Departments of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok - Indonesia)



Article Info

Publish Date
28 Apr 2025

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.

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Journal Info

Abbrev

ejgta

Publisher

Subject

Electrical & Electronics Engineering

Description

The Electronic Journal of Graph Theory and Applications (EJGTA) is a refereed journal devoted to all areas of modern graph theory together with applications to other fields of mathematics, computer science and other sciences. The journal is published by the Indonesian Combinatorial Society ...