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Graph theory and molecular orbitals

Application of Sachs theorem

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Abstract

The Sachs theorem [1] is discussed, and Kekulé and Sachs graphs are defined. The simple consequences of Sachs theorem which are of interest in chemistry are presented. Thus, it is shown that the pairing theorem, Hückel (4m+2) rule, and Longuet-Higgins and Dewar rule [2] can be obtained easily with the use of Sachs theorem. The dependence of the number of Kekulé structures on the molecular topology is also shown.

Zusammenfassung

Das Theorem von Sachs [1] wird diskutiert und Kekulé- und Sachs-Graphen werden definiert. Die einfachen Folgerungen aus dem Theorem von Sachs, die in der Chemie von Interesse sind, werden abgeleitet. So wird gezeigt, daß die Paarregel von Coulson und Rushbrooke, die Hückelsche (4m+2)-Regel und die Regel von Longuet-Higgins und Dewar [2] leicht mit dem Sachsschen Theorem erhalten werden können. Die Abhängigkeit der Zahl der Kekulé-Strukturen von der molekularen Topologie wird ebenfalls gezeigt.

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Graovac, A., Gutman, I., Trinajstić, N. et al. Graph theory and molecular orbitals. Theoret. Chim. Acta 26, 67–78 (1972). https://doi.org/10.1007/BF00527654

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