Enumeration of matchings in polygraphs∗
نویسنده
چکیده
The 6-cube has a total of 7174574164703330195841 matchings of which 16332454526976 are perfect. This was computed with a transfer matrix method associated with polygraphs. For polygraphs of 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 of various polygraphs, such as the 4× 4×m-grid. A Mathematica package, GrafPack, is demonstrated and used for computation of matching polynomials, permanents and for generating transfer matrices.
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تاریخ انتشار 2005