On the sd_{b}-critical graphs

A b-coloring of a graph\ G is a proper coloring of its vertices such that each color class contains a vertex that has a neighbor in every other color classes. The b-chromatic number of a graph G, denoted by b(G), is the largest integer k such that G admits a b-coloring with k colors. Let G_{e} be the graph obtained from G by subdividing the edge e . A graph G is sd_{b}-critical if b(G_{e})