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Journal of Mathematical Chemistry

, Volume 46, Issue 1, pp 214–230 | Cite as

Chemical trees minimizing energy and Hosoya index

  • Clemens Heuberger
  • Stephan G. Wagner
Original Paper

Abstract

The energy of a molecular graph is a popular parameter that is defined as the sum of the absolute values of a graph’s eigenvalues. It is well known that the energy is related to the matching polynomial and thus also to the Hosoya index via a certain Coulson integral. It is quite a natural problem to minimize the energy of trees with bounded maximum degree—clearly, the case of maximum degree 4 (so-called chemical trees) is the most important one. We will show that the trees with given maximum degree that minimize the energy are the same that have been shown previously to minimize the Hosoya index and maximize the Merrifield-Simmons index, thus also proving a conjecture due to Fischermann et al. Finally, we show that the minimum energy grows linearly with the size of the trees, with explicitly computable growth constants that only depend on the maximum degree.

Keywords

Energy of graphs Matchings Chemical trees Matching polynomial Hosoya index 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Institut für Mathematik BTechnische Universität GrazGrazAustria
  2. 2.Department of Mathematical SciencesUniversity of StellenboschStellenboschSouth Africa

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