Symmetric graphs - spectra and eigenvectors

John, Peter E. GND; Sachs, Horst GND

Davidson (1981) developed a general procedure, based on group representation theory, for determining the spectra of graphs distinguished by a certain rotational symmetry, with application to molecular graphs. In this paper a more general method, applicable to any arbitrarily arc weighted directed graph that has a non-trivial automorphism, and yielding both eigenvalues and eigenvectors, is developed. The proofs, elementary and straightforward, avoid the use of the theory of group characters altogether.

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John, Peter E. / Sachs, Horst: Symmetric graphs - spectra and eigenvectors. 2012.

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