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Títol: Edge distance-regular graphs
Autor: Cámara Vallejo, Marc
Dalfó Simó, Cristina
Fàbrega Canudas, José
Fiol Mora, Miquel Àngel
Garriga Valle, Ernest
Altres autors/autores: Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
Matèries: Àrees temàtiques de la UPC::Matemàtiques i estadística
Graph theory
Grafs, Teoria de
Tipus de document: Article
Descripció: Edge-distance-regularity is a concept recently introduced by the authors which is similar to that of distance-regularity, but now the graph is seen from each of its edges instead of from its vertices. More precisely, a graph Γ with adjacency matrix A is edge-distance-regular when it is distance-regular around each of its edges and with the same intersection numbers for any edge taken as a root. In this paper we study this concept, give some of its properties, such as the regularity of Γ, and derive some characterizations. In particular, it is shown that a graph is edge-distance-regular if and only if its k-incidence matrix is a polynomial of degree k in A multiplied by the (standard) incidence matrix. Also, the analogue of the spectral excess theorem for distance-regular graphs is proved, so giving a quasi-spectral characterization of edge-distance-regularity. Finally, it is shown that every nonbipartite graph which is both distance-regular and edge-distance-regular is a generalized odd graph.
* distance-regularity; * local spectra; * predistance polynomials; * the spectral excess theorem; * generalized odd graphs
Altres identificadors i accés: Camara, M. [et al.]. Edge distance-regular graphs. "Electronic notes in discrete mathematics", 2011, vol. 38, p. 221-226.
1571-0653
http://hdl.handle.net/2117/14502
Disponible al dipòsit:E-prints UPC
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