engleski

Simplified Computation of Matchings in Polygraphs

Matching polynomial and perfect matchings for fasciagraphs, rotagraphs and twisted rotagraphs are treated in the paper. Classical transfer matrix method 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 linking edges between monographs. Novel transfer matrices are introduced whose order is much lower tha that in classical transfer matrices. The virtue of the method introduced is especially pronounced when two or 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.

polygraphs; matching polynomial; matchings; perfect matchings; Kekule structures; extended structures; recursive enumeration; transfer matrix method

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