Abstract
The concept of resonant (or Clar) pattern is extended to a plane non-bipartite graph G in this paper: a set of disjoint interior faces of G is called a resonant pattern if such face boundaries are all M-conjugated cycles for some 1-factor (Kekule structure or perfect matching) M of G. In particular, a resonant pattern of benzenoids and fullerenes coincides with a sextet pattern. By applying a novel approach, the principle of inclusion and exclusion in combinatorics, we show that for any plane graphs, 1-factor count is not less than the resonant pattern count, which generalize the corresponding results in benzenoid systems and plane bipartite graphs. Applications to fullerenes are also discussed.
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