A comparison between 1-factor count and resonant pattern count in plane non-bipartite graphs

作者：Zhang HP^*; He JH

来源：Journal of Mathematical Chemistry, 2005, 38(3): 315-324.

DOI：10.1007/s10910-005-5821-x

• plane graph
• fullerene
• benzenoid
• Kekule structure
• resonant pattern

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.

• 出版日期2005-10
• 单位兰州大学