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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Detalles Bibliográficos
Autor: Fiol Mora, Miquel Àngel|||0000-0003-1337-4952
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
Descripción
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.