Theoretica chimica acta

, Volume 60, Issue 3, pp 203–226 | Cite as

Cyclic conjugation and the hückel molecular orbital model

  • I. Gutman
  • O. E. Polansky
Original Investigations


A new graphic polynomial, μ (G, t), has been introduced which depends on a vectort and which reduces to the characteristic and matching polynomial of the graphG for certain choices oft. This leads to a unification of a great part of the previously developed theories of the characteristic and matching polynomials. The basic properties of μ (G, t) are determined.

A method has been developed by which a functionJ (t) can be associated with every π-electron indexJ. Since the componentt a of the vectort is interpreted as the extent by which a particular cycleZa of the molecular graphG influences the polynomial μ(G, t), it is possible to use the functionJ(t) in the study of the effect ofZa on the π-electron indexJ.

Total π-electron energy, π-electron charge and π-electron bond order have been analysed by this method and a number of topological rules of the modulo 4 type have been formulated. It is indicated that all these rules have a common algebraic background.

Key words

Graph theory Hückel rule 


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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • I. Gutman
    • 1
  • O. E. Polansky
    • 1
  1. 1.Max-Planck-Institut für StrahlenchemieMülheim a.d. RuhrGermany

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