$b$-Chromatic number of Some Splitting Graphs (Journal of Informatics and Mathematical Sciences, 2015)
A $b$-colouring of a graph $G$ is a proper vertex colouring of $G$ such that each colour class contains a vertex that has atleast one neighbour in every other colour class and $b$-chromatic number of a graph $G$ is the largest integer $φ(G)$ for which $G$ has a $b$-colouring with $φ(G)$ colours. In this paper, we have obtained the $b$-chromatic number of the splitting graphs of path $P_n$, cycle $C_n$, star $K_{1,n}$, fan graph $F_n$, triangular snake $T_n$, the $H$-graph $H_n$, the corona graph $P_n° K_1$ and $C_n° K_1$.
Keywords: $b$-colouring; $b$-chromatic number