On $$b$$ b -chromatic number with other types of chromatic numbers on double star graphs

Abstract

In this paper, we obtain the $$b$$ -chromatic number for the central graph, middle graph, total graph and line graph of double star graph $$K_{1,n,n}$$ denoted by $$C(K_{1,n,n}), M(K_{1,n,n}), T(K_{1,n,n})$$ and $$L(K_{1,n,n})$$ respectively. We find a relationship between the $$b$$ -chromatic number and three other coloring parameters, the equitable chromatic number, harmonious chromatic number and the achromatic number. Also we conjecture that the $$b$$ -chromatic number is bounded by the harmonious chromatic number.