Maximal resonance of cubic bipartite polyhedral graphs

Wai Chee SHIU, Heping Zhang, Saihua Liu

Research output: Contribution to journalJournal articlepeer-review

8 Citations (Scopus)


Let H be a set of disjoint faces of a cubic bipartite polyhedral graph G. If G has a perfect matching M such that the boundary of each face of H is an M-alternating cycle (or in other words, G - H has a perfect matching), then H is called a resonant pattern of G. Furthermore, G is k-resonant if every i (1 ≤ i ≤ k) disjoint faces of G form a resonant pattern. In particular, G is called maximally resonant if G is k-resonant for all integers k ≥ 1. In this paper, all the cubic bipartite polyhedral graphs, which are maximally resonant, are characterized. As a corollary, it is shown that if a cubic bipartite polyhedral graph is 3-resonant then it must be maximally resonant. However, 2-resonant ones need not to be maximally resonant.

Original languageEnglish
Pages (from-to)676-686
Number of pages11
JournalJournal of Mathematical Chemistry
Issue number3
Publication statusPublished - 2010

Scopus Subject Areas

  • Chemistry(all)
  • Applied Mathematics

User-Defined Keywords

  • Cyclical edge-connectivity
  • k-resonant
  • Polyhedral graph


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