Tomaž Pisanski: Seminar za diskretno matematiko 24.11.2009

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HOMO-LUMO maps of chemical graphs.

Any graph may be represented as a point in the HOMO-LUMO map, ie. the plane determined by the middle two eigenvalues of its adjacency matrix. We define the HL-index of G as the maximal absolute value of the middle two eigenvalues of G. We prove that the HL-index of a chemical tree is bounded by 1. The experiments show that the same bound is valid for most chemical graphs. We investigate similar bounds for more general graph families. In particular we may express some properties of HOMO-LUMO maps using their convex hulls.

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Seminar za diskretno matematiko

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