Department of Mathematics
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.
Journal of Mathematical Chemistry
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benzenoid, Kekulé structure, Clar pattern, plane bipartite graph, normal component
Shiu, Wai Chee, Peter Che Bor Lam, Fuji Zhang, and Heping Zhang. "Normal components, Kekulé patterns, and Clar patterns in plane bipartite graphs." Journal of Mathematical Chemistry 31.4 (2002): 405-420.