b-Chromatic Number of the Graph Power of the Star Graph

In this paper we focus on the newly introduced b-colorings of a graph G. A b-coloring is a proper coloring such that for each color class, there exists at least one vertex which is adjacent to every other color. The b-chromatic number of a graph G is the largest number k such that G admits a b-coloring with k colors. This paper will introduce the b-chromatic number of some interesting graphs. Several operations of graphs are defined, and the b-chromatic number of those operations are found. All graphs in this paper are simple, connected, non-regular graphs. In our main result we compute the b-chromatic number of the graph power of a star.