Abstract: Let be the class of the amply-regular
graphs of parameters where n
is the order, k is the degree, l is
the number of common neighbors of adjacent vertices and those at distance 2 have
two common neighbors. is the class of the
quasi-amply-regular graphs where a pair of adjacent vertices has or common neighbors; such a graph is
defined by parameters The b-chromatic
number of a graph G is defined as the
maximum number k of colors that can be
used to color the vertices of G, such
that we obtain a proper coloring and each color i,
with has at least one
representant adjacent to a vertex of every color
j, We give in this paper some general
properties of this parameter, and we elaborate some bounds of the b-chromatic
number of the Hamming and generalized Hamming graphs.
