Vertex Coloring Edge-Weighting of Some Wheel Related of Graphs

Let G = (V, E) be a connected, undirected and simple graph. For k is an element of N, let w : E(G). {1,2,....,k} be an integer edge-weighting of a graph G. An edge-weighting w induces a vertex coloring f(w) : V(G) -> N defined by fw(v) = Sigma(v is an element of e) w(e). An edge-weighting is called vertex coloring if f(w)(u) not equal f(w)(v) for any edge uv, denoted by mu(G). The minimum k for which G has a vertex-coloring k-edge-weighting. In this paper, our results include lower bound of vertex coloring edge weighting of G + K-1 and the exact value of vertex coloring edge-weighting of some wheel related graphs include fan, friendship, wheel, helm, flower, sun folwer, and closed helm graph.