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Abstract: Matching polynomial and perfect matchings for fasciagraphs, rotagraphs and twisted rotagraphs are treated in the paper. Classical transfer matrix approach makes it possible to get recursions for matching polynomial and perfect matchings, but the order of the matrix grows exponentially in the number of the linking edges between monographs. Novel transfer matrices are introduced whose order is much lower than that in classical transfer matrices. The virtue of the method introduced is especially pronounced when twoor more linking edges end in the same terminal vertex of a monograph. An example of a polyacene polygraph with extended pairings is given where a novel matrix has only 16 entries as compared to 65536 entries in the classical transfer matrix. However, all pairings are treated here on equal footing, but the method introduced can be applied to selected types of pairings of interest in chemistry.
Keywords: polygraphs, matching polynomial, matchings, perfect matchings, Kekulé structures, extended structures, recursive enumeration, transfer matrix method
Published in DKUM: 05.07.2017; Views: 1583; Downloads: 92
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Abstract: An algorithm for computing the algebraic structure count in polygraphs is presented. It expresses the related determinant of the adjacency matrix of a polygraph in terms of the determinants of monographs and bonding edges between the monographs. The algorithm is illustrated on a class of polygraphs with two bonding edges between monographs and computations for selected examples of polygraphs of this class are presented.
Keywords: mathematics, determinant, algebraic structure count, polygraphs, acenylenes, phenylenes
Published in DKUM: 05.07.2017; Views: 1036; Downloads: 128
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