#### Bipartite graphs related to mutually disjoint S-permutation matrices

##### Krasimir Yordzhev

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 $g=$, 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.

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