Let G = (V, E) be a graph. A proper k-coloring of graph G is r-dynamic coloring if for every v, the neighbors of vertex v receive at least min { r, d(v) } different colors. The minimum k such that graph G has r-dynamic ...

In this paper we will study the r-dynamic chromatic number of the coronation by complete graph. A proper k-coloring of graph G such that the neighbors of any vertex v receive at least minfr; d(v)g di®erent colors. The ...

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 ...