Some results of f-critical graph

An f-coloring of a graph G is a coloring of edges of E(G) such that each color appears at each vertex v ∈ V (G) at most f(v) times. The minimum number of colors needed to f-color G is called the f-chromatic index of G, and denoted by χ´f(G). Any graph G has f-chromatic index equal to Δf (G) or Δf(G)+1, where Λf(G)= max_v∈V{⌈d(v)/f(v)⌉}. If χ´f(G) = Δf(G), then G is of Cf 1; otherwise G is of Cf 2. In this paper we give the definition of f-critical and some results for f-coloring of graphs.