Given G, b - coloring is a proper k coloring of G in which each and every color class has at least one b - vertex that has a neighbour in other k - 1 color classes. The largest integer k is the b - chromatic number b(G) for which G having a b - coloring using k colors. In this paper, we constructed some family of graphs and found its b - chromatic number. © Published under licence by IOP Publishing Ltd.