On Maximum Matchings and Eigenvalues of Benzenoid Graphs

Fajtlowicz, Siemion; John, Peter E. GND; Sachs, Horst GND

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.

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Fajtlowicz, S., John PD Dr. rer. nat. habil., P.E., Sachs Prof. Dr. rer. nat. habil. (i.R.), H., 2005. On Maximum Matchings and Eigenvalues of Benzenoid Graphs. Preprint /  Technische Universität Ilmenau, Institut für Mathematik, Preprint /  Technische Universität Ilmenau, Institut für Mathematik 05–07.
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