Computation of matching polynomials and the number of 1-factors in polygraphs

The number of 1-factors in the 6-cube is 16 332 454 526 976. This was computed with the traditional permanent and also with a transfer matrix approach, associated with polygraphs. For polygraphs of the type G×Pm we present a method for compression of the transfer matrix. This compression gives a substantial reduction of the order of the transfer matrix by exploiting the automorphisms of the graph G. We compute and tabulate matching polynomials and the number of 1-factors in various polygraphs, such as the 4× 4×m-grid. A Mathematica package for computing matching polynomials, permanents and generating transfer matrices etc is listed at the end of the paper.