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All Journal Indonesian Journal of Combinatorics
Chandra, Ivana Joice
University Indonesia
Computer Science & IT Decision Sciences, Operations Research & Management

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Local edge antimagic coloring for chain of path and cycle Walfried, Yosua; Chandra, Ivana Joice; Silaban, Denny Riama
Indonesian Journal of Combinatorics Vol 9, No 1 (2025)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2025.9.1.2

Abstract

Let G=(V,E) be a simple connected graph with vertex set V and edge set E. A local edge antimagic labeling of G is a bijection f:V (G)→{1, 2, 3, ... , |V(G)|} where the weights of any two adjacent edges of G are distinct. The weight of an edge uv is defined as w(uv) = f(u)+f(v). By assigning the color w(uv) to each edge uv ∈ E(G), we obtain a proper local edge antimagic coloring of G. The minimum number of colors required for edge coloring induced by the local edge antimagic labeling is called a local antimagic chromatic index of G. In this article, we give the exact value of the local antimagic chromatic index for the chain of path and cycle graphs.
Co-Authors Silaban, Denny Riama Walfried, Yosua