r-Dynamic Coloring of the Corona Product of Graphs

Abstract

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.