Local edge antimagic coloring for chain of path and cycle

Walfried, Yosua (University Indonesia)
Chandra, Ivana Joice (University Indonesia)
Silaban, Denny Riama (University Indonesia)

Indonesian Journal of Combinatorics
Vol 9, No 1 (2025)

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.