Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

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.

Keywords

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

Publication Date

2002

Source Publication Title

Journal of Mathematical Chemistry

Volume

31

Issue

4

Start Page

405

End Page

420

Publisher

Springer Verlag

Peer Reviewed

1

DOI

10.1023/A:1021072722165

Link to Publisher's Edition

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

ISSN (print)

15728897

Included in

Mathematics Commons

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