  Some numerical characteristics of bipartite graphs in relation to the problem
of finding all disjoint pairs of S-permutation matrices in the general $n^2
\times n^2$ case are discussed in this paper. All bipartite graphs of the type
$g=<R_g \cup C_g, E_g>$, where $|R_g |=|C_g |=2$ or $|R_g |=|C_g |=3$ are
provided. The cardinality of the sets of mutually disjoint S-permutation
matrices in both the $4 \times 4$ and $9 \times 9$ cases are calculated.

Combinatorics;Discrete Mathematics