A simple proof of the spectral excess theorem for distance-regular graphs |
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Authors: | M.A. Fiol S. Gago |
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Affiliation: | a Dep. Matemàtica Aplicada IV, Universitat Politècnica de, Catalunya, Jordi Girona 1-3, Mòdul C3, Campus Nord, 08034 Barcelona, Catalonia, Spain b Dep. Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, CIMNE C3, Av. Canal Ol?´mpic s/n, 08860 Castelldefels, Catalonia, Spain |
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Abstract: | The spectral excess theorem provides a quasi-spectral characterization for a (regular) graph Γ with d+1 distinct eigenvalues to be distance-regular graph, in terms of the excess (number of vertices at distance d) of each of its vertices. The original approach, due to Fiol and Garriga in 1997, was obtained by using a local approach, so giving a characterization of the so-called pseudo-distance-regularity around a vertex. In this paper we present a new simple projection method based in a global point of view, and where the mean excess plays an essential role. |
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Keywords: | Distance-regular graph Adjacency matrix Spectrum Predistance polynomials Excess |
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