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On the construction of the matching polynomial for unbranched catacondensed benzenoids
Author(s) -
Randić Milan,
Hosoya Haruo,
Polansky Oskar E.
Publication year - 1989
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540100510
Subject(s) - multiplication (music) , combinatorics , mathematics , rank (graph theory) , polynomial , matching (statistics) , hexagonal crystal system , benzene , discrete mathematics , chemistry , crystallography , organic chemistry , mathematical analysis , statistics
An algorithm for obtaining the matching polynomial of an arbitrary catacondensed unbranched benzenoid molecule is presented. It is based on multiplication of only three 5 x 5 transfer matrices I , J , K , and an appropriate terminal vector. The choice of the matrices is dictated by the history of the growth of the hexagonal “animals” (i.e., by the pattern of the successive fusions of the benzene rings). The approach also gives the number of Kekule valance structures, the count of conjugated circuits, the values of the topological index Z , and the characteristic polynomials.