A new approach to the spectral excess theorem for distance-regular graphs
The Spectral Excess Theorem provides a quasi-spectral characterization for a (regular) graph $\Gamma$ with $d+1$ different eigenvalues to be distance-regular graph, in terms of the mean (d-1)-excess of its vertices.\ The original approach, due to Fiol and Garriga in $1997$, was obtained in a wide co...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2009 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/2823 |
| Acceso en línea: | https://hdl.handle.net/2117/2823 |
| Access Level: | acceso abierto |
| Palabra clave: | Graph theory Matrices Distance-regular graphs Eigenvalues Excess Grafs, Teoria de Matrius (Àlgebra) Classificació AMS::05 Combinatorics::05C Graph theory Classificació AMS::15 Linear and multilinear algebra matrix theory Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | The Spectral Excess Theorem provides a quasi-spectral characterization for a (regular) graph $\Gamma$ with $d+1$ different eigenvalues to be distance-regular graph, in terms of the mean (d-1)-excess of its vertices.\ The original approach, due to Fiol and Garriga in $1997$, was obtained in a wide context from a local point of view, so giving a characterization of the so-called pseudo-distance-regularity around a vertex.\ In this paper we present a new simple method based in a global point of view, and where the mean degree of the distance-$d$ graph $\Gamma_d$ plays an essential role. |
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