Perfect 3-colorings of the Johnson graphs J (4,2), J (5,2), J (6,2) and Petersen graph

A perfect m-coloring of a graph G with a matrix A = {a(ij)}(i,j) = (1), ... , (m) is a coloring of the vertices of G into the set of colors {1, ... , m} such that, for all i, j is an element of {1, ... , m}, every vertex of color i is adjacent to exactly vertices of color j. The matrix A is called the parameter matrix of a perfect coloring. In this paper, three common propositions of perfect 2-colorings are generalized for perfect m-colorings. Then, three general constructions of perfect colorings are introduced. After all, the parameter matrices of all perfect 3-colorings of the Johnson graphs J (4, 2), J (5, 2), J (6, 2) and Petersen graph are listed.