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Simplified computation of matchings in polygraphs

Graovac, Ante; Vukičević, Damir; Ježek, Damir; Žerovnik, Janez (2005) Simplified computation of matchings in polygraphs. Croatica Chemica Acta, 78 (2). pp. 283-287. ISSN 0011-1643

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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 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.

Item Type: Article
Uncontrolled Keywords: polygraphs; matching polynomial; matchings; perfect matchings; Kekule structures; extended structures; recursive enumeration; transfer matrix method; resonance energies; rotagraphs; polymers
Subjects: NATURAL SCIENCES > Chemistry
Divisions: NMR Center
Project titleProject leaderProject codeProject type
Modeliranje novih ugljikovih materijalaAnte Graovac0098039MZOS
Diskretna matematika i primjeneDragutin Svrtan0037117MZOS
Depositing User: Virna Brumnić
Date Deposited: 06 Nov 2013 12:18

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