r-Dynamic coloring of the corona product of graphs

Abstract

Let [Formula: see text] be a graph. A proper [Formula: see text]-coloring of graph [Formula: see text] is [Formula: see text]-dynamic coloring if for every [Formula: see text], the neighbors of vertex [Formula: see text] receive at least min[Formula: see text] different colors. The minimum [Formula: see text] such that graph [Formula: see text] has [Formula: see text]-dynamic [Formula: see text] coloring is called the [Formula: see text]-dynamic chromatic number, denoted by [Formula: see text]. In this paper, we study the [Formula: see text]-dynamic coloring of corona product of graph. The corona product of graph is obtained by taking a number of vertices [Formula: see text] copy of [Formula: see text], and making the [Formula: see text]th of [Formula: see text] adjacent to every vertex of the [Formula: see text]th copy of [Formula: see text]. We obtain the lower bound of [Formula: see text]-dynamic chromatic number of corona product of graphs and some exact value.