R-Dynamic coloring of the corona product of graphs

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 k coloring is called the r-dynamic chromatic number, denoted by χr(G). In this paper, we study the r-dynamic coloring of corona product of graph. The corona product of graph is obtained by taking a number of vertices |V (G)| copy of H, and making the ith of V (G) adjacent to every vertex of the ith copy of V (H). We obtain the lower bound of r-dynamic chromatic number of corona product of graphs and some exact value.