On the r-dynamic chromatic number of the corronation by complete graph

Abstract

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 min{r, d(v)} different colors. The r-dynamic chromatic number, χr(G) is the minimum k such that graph G has an r-dynamic k-coloring. We will obtain lower bound of the r-dynamic chromatic number of , and We also study the exact value of the r-dynamic chromatic number of and for m, n > 3.