All graphs in this paper are nontrivial and connected graph. Let 𝑓 ∶ 𝑉 (𝐺) → *1,2, … , 𝑘+ be a vertex coloring of a graph 𝐺where two adjacent vertices may be colored the same color. Consider the color classes Π = ...

All graph in this paper is connected graph. Let du,v be a distance between any vertex u and v in graph GV,E. A function c :VG 1, 2, , k is called a packing k  coloring if every two vertex of color i are ...