ON NONEXISTENCE OF SOME PERFECT 2-COLORINGS OF JOHNSON GRAPHS.
A perfect coloring in m colors of a graph <i>G </i>with matrix <i>A = {a</i><sub><i>i</i>j</sub>}<sub>i<i>j</i></sub><i>=1,...,</i><sub><i>m</i></sub><i> </i>is a coloring of vertex set of <i>G </i>in the set of colors {1,..., m} such that the number of vertices of color <i>j </i>adjacent to a fixed vertex of color <i>i </i>does not depend on choice of the last vertex and equals a<sub>ij</sub><i>. </i>In this paper we obtain a low bound on parameter <i>a</i><sub><i>ij</i></sub><i>,i ≠ j, </i>of a perfect coloring of a Johnson graph in two colors. Also we show that some perfect colorings of Johnson graph in two colors do not exist.