Journal of Mathematical Chemistry

, Volume 42, Issue 4, pp 1041–1056 | Cite as

Double hexagonal chains with minimal total π-electron energy

  • Haizhen Ren
  • Fuji Zhang

The total energy of all π-electrons in a conjugated hydrocarbon (within the framework of HMO approximation) is the sum of the absolute value of all the eigenvalues of its corresponding graph. In this paper, we consider “double hexagonal chains” as benzenoids constructed by successive fusions of successive naphthalenes along a zig–zag sequence of triples of edges as appear on opposite sides of each naphthalene unit. It is shown that if the fusions are such as to give a polyaceacene then the total π-electron energy is the minimum from among all the double hexagonal chains with the same number of naphthalene units.


the total π-electron energy double hexagonal chain quasi-ordering 

AMS subject classification

05C50 05C35 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of MathematicsQinghai Normal UniversityXining, QinghaiP.R. China
  2. 2.School of Mathematical SciencesXiamen UniversityXiamen, FujianP.R. China

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