Local edge antimagic coloring for chain of path and cycle

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.