Algebraic characterizations of distance-regular graphs
We survey some old and some new characterizations of distance-regular graphs, which depend on information retrieved from their adjacency matrix. In particular, it is shown that a regular graph with d+1 distinct eigenvalues is distance-regular if and only if a numeric equality, involving only the spe...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2002 |
| 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:2117/2238 |
| Acceso en línea: | https://hdl.handle.net/2117/2238 |
| Access Level: | acceso abierto |
| Palabra clave: | Graph theory Distance-regular graph Adjacency matrix Spectrum Grafs, Teoria de Classificació AMS::05 Combinatorics::05C Graph theory |
| Sumario: | We survey some old and some new characterizations of distance-regular graphs, which depend on information retrieved from their adjacency matrix. In particular, it is shown that a regular graph with d+1 distinct eigenvalues is distance-regular if and only if a numeric equality, involving only the spectrum of the graph and the numbers of vertices at distance d from each vertex, is satisfied. |
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