20.500.12556/DKUM-66667 Simplified computation of matchings in polygraphs Pojednostavljeni račun sparivanja u poligrafovima 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. U radu se razmatraju polinomi sparivanja i savršena sparivanja u fascia- i rotagrafovima te izvijenim rotagrafovima. Iako klasični postupak transfer matrice omogućava izvođenje rekurzija za polinom sparivanja i savršena sparivanja, red ove matrice eksponencijalno raste s brojem veza među monografovima. Ovdje su uvedene nove transfer matrice čiji je red mnogo niži od onoga za klasične transfer matrice, i to posebice kada jedna ili više veza među monografovima završava u jednom te istom čvoru. Postupak je ilustriran na primjeru poliacenskih poligrafova gdje ovdje uvedena matrica ima samo 16 elemenata u usporedbi s 65536 elemenata klasične transfer matrice. Iako se ovdje uvedeni postupak primjenjuje istovremeno na sva moguća sparivanja u poligrafovima, on je otvoren za primjenu na odabrana sparivanja od posebnoga kemijskoga interesa. polygraphs matching polynomial matchings perfect matchings Kekulé structures extended structures recursive enumeration transfer matrix method poligrafi polinomi ujemanje popolno ujemanje Kekuléjeve strukture razširjene strukture rekurzivno štetje true false true Angleški jezik Hrvaški jezik Znanstveno delo 2017-07-05 12:00:19 2017-07-05 12:01:31 2022-08-01 13:01:39 2019-07-11 15:54:56 2005 0 0 str. 283-287 št. 2 Letn. 78 2005 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 0011-1643 51:54 22807 9736726 0011-1643 URN:SI:UM:DK:RZAK6L6J Croatica_Chemica_Acta_2005_Graovac_et_al._Simplified_computation_of_matchings_in_polygraphs.pdf Croatica_Chemica_Acta_2005_Graovac_et_al._Simplified_computation_of_matchings_in_polygraphs.pdf 1 CB47131CE0AA8C98B3526F9ED85900D6 b34a87a75fff690fa72a23024b751c9e248d7771a6a1afd300c42ca246cdb9c6 5bbec9d1-7c0e-11eb-bb7a-00155d0001ca 20.500.12556/dkum/8e6ddd5f-2c37-4cf6-b978-85212a530b87 https://dk.um.si/Dokument.php?lang=slv&id=113683 http://hrcak.srce.hr/23 1 https://dk.um.si/Dokument.php?lang=slv&id=113682 Fakulteta za strojništvo 0 0 0