  In the present paper we calculate the Gromov-Hausdorff distance between an
arbitrary simplex (a metric space all whose non-zero distances are the same)
and a finite metric space whose non-zero distances take two distinct values
(so-called $2$-distance spaces). As a corollary, a complete solution to
generalized Borsuk problem for the $2$-distance spaces is obtained. In
addition, we derive formulas for the clique covering number and for the
chromatic number of an arbitrary graph $G$ in terms of the Gromov-Hausdorff
distance between a simplex and an appropriate $2$-distance space constructed by
the graph $G$.
