Document Type

Journal Article

Department/Unit

Department of Mathematics

Abstract

As a general case of molecular graphs of polycyclic alternant hydrocarbons, we consider a plane bipartite graph G with a Kekulé pattern (perfect matching). An edge of G is called nonfixed if it belongs to some, but not all, perfect matchings of G. Several criteria in terms of resonant cells for determining whether G is elementary (i.e., without fixed edges) are reviewed. By applying perfect matching theory developed in plane bipartite graphs, in a unified and simpler way we study the decomposition of plane bipartite graphs with fixed edges into normal components, which is shown useful for resonance theory, in particular, cell and sextet polynomials. Further correspondence between the Kekulé patterns and Clar (resonant) patterns are revealed.

Publication Year

2002

Journal Title

Journal of Mathematical Chemistry

Volume number

31

Issue number

4

Publisher

Springer Verlag

First Page (page number)

405

Last Page (page number)

420

Referreed

1

DOI

10.1023/A:1021072722165

ISSN (print)

15728897

Link to Publisher’s Edition

https://dx.doi.org/10.1023/A:1021072722165

Keywords

benzenoid, Kekulé structure, Clar pattern, plane bipartite graph, normal component

Included in

Mathematics Commons

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