Journal of Mathematical Chemistry

, Volume 12, Issue 1, pp 265–277 | Cite as

Graphs corresponding to reference polynomial or to circuit characteristic polynomial

  • Noriyuki Mizoguchi
Article

Abstract

A vertex-weighted graphG* is studied which is obtained by deleting edgee rs in a circuit of a graphG and giving two vertices νr and εs weightsh r = 1 andh s = -1, respectively. It is shown that if subgraphG - νr is identical with subgraphG - νs, then the reference polynomial ofG* is identical with that ofG and the characteristic polynomial ofG* contains the contributions due to only a certain part of the circuits found in the original graphG. This result gives a simple way to find a graph whose characteristic polynomial is equal to the reference polynomial in the topological resonance energy theory or to the circuit characteristic polynomial in the circuit resonance energy theory. This approach can be applied not only to Hilckel graphs but also to Möbius graphs, provided that they satisfy a certain condition. The significances of this new type of “reference” graph thus obtained are pointed out.

Keywords

Physical Chemistry Resonance Energy Characteristic Polynomial Energy Theory Topological Resonance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© J.C. Baltzer AG, Science Publishers 1993

Authors and Affiliations

  • Noriyuki Mizoguchi
    • 1
  1. 1.Department of PhysicsMeiji College of PharmacyNozawaJapan

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