On Maximum Matchings and Eigenvalues of Benzenoid Graphs

By S. Fajtlowicz, P. John, H. Sachs. 2005

46 citations recorded by the source corpus.

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.

View Paper: https://www.semanticscholar.org/paper/7c00abcb9162e83149f126c75a284ed2505d86b2

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1. Richard Koryt'ar
2. S. Tewari
3. F. Evers
4. J. V. van Ruitenbeek
5. O. Yazyev
6. D. Papageorgiou
7. D. Pesin

Citations in the corpus

• Advances and challenges in single-molecule electron transport (2019, background): “The result was sharpened later in benzoidal graph theory: the equal-sign holds for honeycomb lattices (Fajtlowicz et al., 2005).”
• Emergence of magnetism in graphene materials and nanostructures (2010, methodology): “The spectrum of the tight-binding Hamiltonian of a honeycomb system can be analyzed using a mathematically rigorous approach of the benzenoid graph theory (Fajtlowicz et al., 2005).”