Original scientific paper

On Maximum Matchings and Eigenvalues of Benzenoid Graphs

Siemion Fajtlowicz
Peter E. John
Horst Sachs

Abstract

In August 2003 the computer program GRAFFITI made conjecture 1001 stating that for any benzenoid graph, the size of a maximum matching equals the number of positive eigenvalues. Later, the authors learned that this conjecture was already known in 1982 to I. Gutman (Kragujevac). Here we present a proof of this conjecture and of a related theorem. The results are of some relevance in the theory of (unsaturated) polycyclic hydrocarbons.

Keywords

benzenoid graph; characteristic polynomial and spectrum of graphs; hexagonal systems; Hückel-MO-Theory; resonance theory

Hrčak ID:

12

URI

https://hrcak.srce.hr/12

Publication date:

15.6.2005.

Article data in other languages: croatian

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