The problem on f -coloring of all generalized petersen graphs

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 Δf (G) = max_veV{[d(v)/f(v)]}. If χ´f(G) = Δf(G), then G is of Cf 1; otherwise G is of Cf 2. The f-core of G is the subgraph of G induced by the vertices of V0* ={v:Δf(G)=d(v)/f(v),v ∈ V(G)}. In this paper some results about the generalized Petersen graphs are presented.