05828850

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05828850 Vuki\v{c}evi\'c, Damir Applications of perfect matchings in chemistry. Dehmer, Matthias (ed.), Structural analysis of complex networks. Basel: Birkh\"auser (ISBN 978-0-8176-4788-9/hbk; 978-0-8176-4789-6/ebook). 463-482 (2011). 2011 Basel: Birkh\"auser EN perfect matching Kekul\'e structure Pfaffian enumeration resonance graph anti-Kekul\'e number

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

Summary: Perfect matchings or one factors in mathematics correspond to Kekul\'e 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 (Kekul\'e structures) is illustrated with several different chemical applications. A method for coding Kekul\'e structures which enables efficient storing in the computer is presented. Also, the recently introduced notion of algebraic Kekul\'e structures is explained and its role in the classification of Kekul\'e 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.