### Abstract

We introduce the concept of a forcing hexagon in a hexagonal system H, which is a hexagon h in H such that the subgraph of H obtained by deleting all vertices of h together with their incident edges has exactly one perfect matching. We show that any hexagonal system with a forcing hexagon is a normal hexagonal system. We further prove that every hexagon of a hexagonal system H is forcing if and only if H is a linear hexagonal chain, and that any other hexagonal system has at most two forcing hexagons. Using the tool of Z-transformation graphs developed by F. Zhang et al, we prove the co-existence property of forcing hexagons and forcing edges, and we obtain the structural characterizations for the hexagonal systems with a given number of forcing hexagons. Miscellaneous related results are presented. We also post a question for further investigation.

Original language | English (US) |
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Pages (from-to) | 649-668 |

Number of pages | 20 |

Journal | Match |

Volume | 56 |

Issue number | 3 |

State | Published - Dec 1 2006 |

### All Science Journal Classification (ASJC) codes

- Chemistry(all)
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics