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Applications of Perfect Matchings in Chemistry

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Structural Analysis of Complex Networks

Abstract

Perfect matchings or one factors in mathematics correspond to Kekulé structures in chemistry. In this chapter, we present methods for determination of the existence and enumeration of perfect matchings. The Pfaffian method of enumeration of perfect matchings in planar graphs is presented. The importance of the enumeration of perfect matchings (Kekulé structures) is illustrated with several different chemical applications. A method for coding Kekulé structures which enables efficient storing in the computer is presented. Also, the recently introduced notion of algebraic Kekulé structures is explained and its role in the classification of Kekulé structures according to their significance is discussed. The concept of the resonance graph is presented and its role in the study of fullerene molecules is commented.

MSC2000: Primary 05C70; Secondary 05C90, 05C85

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Acknowledgments

Partial support of the Ministry of Science, Education and Sports of the Republic of Croatia is gratefully acknowledged (grant no. 177–0000000-0884 and grant no. 037-0000000-2779).

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Authors and Affiliations

  1. Faculty of Mathematics and Natural Sciences, University of Split, Nikole Tesle 12, HR-21000, Split, Croatia

    Damir Vukičević

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  1. Damir Vukičević
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Correspondence to Damir Vukičević .

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  1. Medizinische Informatik und Technik, Institute for Bioinformatics and Transla, UMIT-Private Universität für Gesundheits, Eduard Wallnöfer-Zentrum 1, Hall in Tirol, A-6060, Austria

    Matthias Dehmer

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Vukičević, D. (2011). Applications of Perfect Matchings in Chemistry. In: Dehmer, M. (eds) Structural Analysis of Complex Networks. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4789-6_19

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