Forcing hexagons in hexagonal systems

Zhongyuan Che, Zhibo Chen

Research output: Contribution to journalArticle

8 Scopus citations

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 languageEnglish (US)
Pages (from-to)649-668
Number of pages20
JournalMatch
Volume56
Issue number3
StatePublished - Dec 1 2006

All Science Journal Classification (ASJC) codes

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

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  • Cite this

    Che, Z., & Chen, Z. (2006). Forcing hexagons in hexagonal systems. Match, 56(3), 649-668.