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 0 in every vertex v such that v 0 adjacent to v in graph G. An m-splitting graph is a graph which has m v 0 -vertices, denoted by Spl(G). A local edge antimagic coloring in G = (V; E) graph is a bijection f : V (G) ! f1; 2; 3; :::; jV (G)jg in which for any two adjacent edges e 1 and e 2 satis es w(e 1 ) 6 = w(e 2 m ), where e = uv 2 G. The color of any edge e = uv are assigned by w(e) which is de ned by sum of label both end vertices f(u) and f(v). The chromatic number of local edge antimagic labeling

(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.