Original scientific paper

Simplified Computation of Matchings in Polygraphs

Ante Graovac
Damir Vukičević
Damir Ježek
Janez Zerovnik

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 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.

Keywords

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

Hrčak ID:

23

URI

https://hrcak.srce.hr/23

Publication date:

15.6.2005.

Article data in other languages: croatian

Visits: 2.226 *