On the dynamic coloring of graphs

A dynamic coloring of a graph image is a proper coloring such that, for every vertex image of degree at least 2, the neighbors of image 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 image-regular graph image, image. Also, we introduce an upper bound for the dynamic list chromatic number of regular graphs.