Applications of Perfect Matchings in Chemistry

Damir Vukičević ()
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Damir Vukičević: University of Split, Faculty of Mathematics and Natural Sciences

Chapter Chapter 19 in Structural Analysis of Complex Networks, 2011, pp 463-482 from Springer

Abstract: 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.

Keywords: Perfect matching; Kekulé structure; Pfaffian; Enumeration; Resonance graph; Anti-Kekulé number (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-4789-6_19

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DOI: 10.1007/978-0-8176-4789-6_19

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