On the dynamic coloring of graphs

A dynamic coloring of a graph G is a proper coloring such that, for every vertex v@?V(G) of degree at least 2, the neighbors of v receive at least 2 colors. In this paper, we present some upper bounds for the dynamic chromatic number of graphs. In this regard, we shall show that, for every k-regular graph G, @g"2(G)@?@g(G)+14.06lnk+1. Also, we introduce an upper bound for the dynamic list chromatic number of regular graphs.