B-Chromatic number of some cycle related graphs

A textit{b}-coloring by textit{k}-colors is a proper coloring of the vertices of graph $textit{G}$ such that in each color classes there exists a vertex that has neighbours in all the other $k-1$ color classes. The textit{b}-chromatic number $varphi (G)$ is the largest integer $textit{k}$ for which $textit{G}$ admits a textit{b}-coloring with textit{k}-colors. If $chi (G)$ is the chromatic number of $textit{G}$ then $textit{G}$ is said to be textit{b}-continuous if $b$-coloring exists for every integer $k$ satisfying $chi left( G right) le k le varphi left( G right)$. We investigate the textit{b}-chromatic number of some cycle related graphs and also study their textit{b}-continuity.