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 minfr; d(v)g di®erent colors. The r-dynamic chromatic number, Âr(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 Âr(Kn ¯ H), and Âr(H ¯ Km) We also study the exact value of the r-dynamic chromatic number of Âr(Kn ¯ Sm); Âr(Kn ¯ Fm); Âr(Sn ¯ Km); Âr(Fn ¯ Km) and Âr(Kn ¯ Km) for m; n ¸ 3.