This study is a natural extension of k -proper coloring of any simple and connected graph G. By a n rdynamic coloring of a graph G, we mean a proper k coloring of graph G such that the neighbors of any vert ...

A proper k coloring of graph G such that the neighbors of any vertex v ∈ V (G) where at least min{r, d(v)} different colors is defined an r-dynamic coloring. The minimum k such that graph G has an r-dynamic k coloring is ...