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Edge distance-regular graphs
dc.contributor.author | Cámara Vallejo, Marc |
dc.contributor.author | Dalfó Simó, Cristina |
dc.contributor.author | Fàbrega Canudas, José |
dc.contributor.author | Fiol Mora, Miquel Àngel |
dc.contributor.author | Garriga Valle, Ernest |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV |
dc.date.accessioned | 2012-01-13T08:55:44Z |
dc.date.available | 2012-01-13T08:55:44Z |
dc.date.created | 2011 |
dc.date.issued | 2011 |
dc.identifier.citation | Camara, M. [et al.]. Edge distance-regular graphs. "Electronic notes in discrete mathematics", 2011, vol. 38, p. 221-226. |
dc.identifier.issn | 1571-0653 |
dc.identifier.uri | http://hdl.handle.net/2117/14502 |
dc.description | * distance-regularity; * local spectra; * predistance polynomials; * the spectral excess theorem; * generalized odd graphs |
dc.description.abstract | 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. |
dc.format.extent | 6 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística |
dc.subject.lcsh | Graph theory |
dc.title | Edge distance-regular graphs |
dc.type | Article |
dc.subject.lemac | Grafs, Teoria de |
dc.contributor.group | Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
dc.description.peerreviewed | Peer Reviewed |
dc.rights.access | Open Access |
local.identifier.drac | 9368235 |
dc.description.version | Postprint (published version) |
local.citation.author | Camara, M.; Dalfo, C.; Fàbrega, J.; Fiol, M. A.; Garriga, E. |
local.citation.publicationName | Electronic notes in discrete mathematics |
local.citation.volume | 38 |
local.citation.startingPage | 221 |
local.citation.endingPage | 226 |
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