On the local edge antimagicness of m-splitting graphs

Abstract

Let G be a connected and simple graph. A split graph is a graph derived by adding new vertex v0 in every vertex v such that v0 adjacent to v in graph G. An m-splitting graph is a graph which has m v′-vertices, denoted by mSpl(G). A local edge antimagic coloring in G = (V;E) graph is a bijection f : V (G) →{1; 2; 3; ⋯|V (G)|} in which for any two adjacent edges e1 and e2 satisfies w(e1) ≠ w(e2), where e = uv ∈ G. The color of any edge e = uv are assigned by w(e) which is defined by sum of label both end vertices f(u) and f(v). The chromatic number of local edge antimagic labeling lea(G) is the minimal number of color of edge in G graph which has local antimagic coloring. We present the exact value of chromatic number lea of m-splitting graph and some special graphs.