Perfect 2-colorings of the Johnson graph J(9,4)

A perfect 2-coloring of a graph Gamma with matrix M = {m(ij)}(i,j=1,2) is a coloring of the vertices Gamma with colors called {1, 2} such that the number of vertices of color j adjacent to a fixed vertex of color i is equal to m(ij). We state the matrix M is the parameter matrix. Each class of an equitable partition is the vertices with the same color. In this article, we classify the parameter matrices of whole perfect 2-colorings of the Johnson graph J(9, 4).