Journal of Mathematical Chemistry

, Volume 55, Issue 9, pp 1878–1886 | Cite as

Perfect matchings in random pentagonal chains

  • Chuanqi XiaoEmail author
  • Haiyan Chen
  • Lu Liu
Original Paper


Let G be a (molecule) graph. A perfect matching, or kekulé structure and dimer covering, in a graph G is a set of pairwise nonadjacent edges of G that spans the vertices of G. In this paper, we obtained the explicit expression for the expectation of the number of perfect matchings in random pentagonal chains. Our result shows that, for any polygonal chain \(Q_{n}\) with odd polygons, the number of perfect matchings can be determined by their concatenation LA-sequence.


Perfect matching Pentagonal chain Expectation 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Innovation and High TechnologyMoscow Institute of Physicss and TechnologyMoscowRussian Federation
  2. 2.School of ScienceJimei UniversityXiamenPeople’s Republic of China
  3. 3.School of BusinessNankai UniversityTianjinPeople’s Republic of China

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