Bipartite graphs related to mutually disjoint S-permutation matrices

Abstract

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.

18 pages, 13 figures. arXiv admin note: text overlap with arXiv:1211.1628

Cited by in corpus (1)

• On the Number of Disjoint Pairs of S-permutation Matrices