## Abstract

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 language | English |
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Pages (from-to) | 676-686 |

Number of pages | 11 |

Journal | Journal of Mathematical Chemistry |

Volume | 48 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2010 |

## Scopus Subject Areas

- Chemistry(all)
- Applied Mathematics

## User-Defined Keywords

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