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The characteristic polynomial of a chemical graph

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Abstract

We list uses of, and the computational methods for the characteristic polynomial of a (chemical) graph. Pour computational methods are singled out for more detailed presentation. These are the graphical methods of Sachs, the recurrence formulae for several classes of simple graphs, the method based on Ulam subgraphs, and the Le Verrier — Faddeev — Franic recursive method. The latter method appears, at present, to be the most efficient procedure for the computation of the characteristic polynomials of graphs of sizes with up to even a few hundred sites.

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  1. Nenad Trinajstić

    Present address: The Rugjer Bošković Institute, P.O. Box 1016, 41001, Zagreb, Croatia, Yugoslavia

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  1. Department of Marine Sciences, Texas A & M University, 77553, Galveston, Texas, USA

    Nenad Trinajstić

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Dedicated to Dennis H. Rouvray, the friend and one of the foremost popularizers of chemical graph theory in our time.

Research supported by the Robert A. Welch Foundation of Houston, Texas, USA.

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Trinajstić, N. The characteristic polynomial of a chemical graph. J Math Chem 2, 197–215 (1988). https://doi.org/10.1007/BF01167201

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