Vertex coloring of a fuzzy graph using alpa cut

Let G= (V_F, E_F) be a simple connected undirected fuzzy graph where V_F is a fuzzy set of vertices where each vertices has membership value μ and E_F is a fuzzy set of edges where each edge has a membership value σ. Vertex coloring is a function which assigns colors to the vertices so that adjacent vertices receive different colors. In this paper, we introduce a coloring function of fuzzy graph (crisp mode) to color all the vertices of graph of G and find the chromatic number of graph G which is a fuzzy number. The function is based on α cut of graph G. For different value of α cut which is depended on edge and vertex membership value of graph G we will get different graph and different chromatic number.