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 v′ in every vertex v′ such that v′ 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 in which for any two adjacent edges e1 and e2 satisfies , where . 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 γlea(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 γlea of m-splitting graph and some special graphs.