Journal of Mathematical Chemistry

, Volume 54, Issue 2, pp 416–427 | Cite as

Enumeration of cyclic polyazulenoids

  • Kecai DengEmail author
  • Xiaoling Zhang
Original Paper


A cyclic polyazulenoid structure is a kind of nonalternant conjugated hydrocarbon consisting of a cyclic series of alternatingly fused five membered rings and seven membered rings, which forms a “belt of rings” or say, “belt of azulenes”, more precisely. We give the exact counting formula for the number of cyclic polyazulenoid isomers according to the number of azulene units, by a method based on a generalization of Pólya’s Theorem.


Cyclic polyazulenoids Enumeration Pólya’s Theorem 

Mathematics Subject Classification

92E10 05C30 05C90 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.School of Mathematical SciencesHuaqiao UniversityQuanzhouPeople’s Republic of China
  2. 2.School of Mathematical and Computer SciencesQuanzhou Normal UniversityQuanzhouPeople’s Republic of China

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