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The spectral excess theorem for distance-regular graphs having distance-d graph with fewer distinct eigenvalues
dc.contributor.author | Fiol Mora, Miquel Àngel |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2016-04-01T11:00:13Z |
dc.date.available | 2017-11-30T01:30:37Z |
dc.date.issued | 2015-01-01 |
dc.identifier.citation | Fiol, M. The spectral excess theorem for distance-regular graphs having distance-d graph with fewer distinct eigenvalues. "Electronic notes in discrete mathematics", 01 Gener 2015, vol. 49, p. 457-463. |
dc.identifier.issn | 1571-0653 |
dc.identifier.uri | http://hdl.handle.net/2117/85047 |
dc.description.abstract | Let G be a distance-regular graph with diameter d and Kneser graph K=Gd, the distance-d graph of G. We say that G is partially antipodal when K has fewer distinct eigenvalues than G. In particular, this is the case of antipodal distance-regular graphs (K with only two distinct eigenvalues), and the so-called half-antipodal distance-regular graphs (K with only one negative eigenvalue). We provide a characterization of partially antipodal distance-regular graphs (among regular graphs with d distinct eigenvalues) in terms of the spectrum and the mean number of vertices at maximal distance d from every vertex. This can be seen as a general version of the so-called spectral excess theorem, which allows us to characterize those distance-regular graphs which are half-antipodal, antipodal, bipartite, or with Kneser graph being strongly regular. |
dc.format.extent | 7 p. |
dc.language.iso | eng |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria |
dc.subject.lcsh | Graph theory |
dc.subject.lcsh | Combinatorial analysis |
dc.subject.other | Distance-regular graph |
dc.subject.other | Kneser graph |
dc.subject.other | Partial antipodality |
dc.subject.other | Predistance polynomials |
dc.subject.other | Spectrum |
dc.title | The spectral excess theorem for distance-regular graphs having distance-d graph with fewer distinct eigenvalues |
dc.type | Article |
dc.subject.lemac | Teoria de grafs |
dc.subject.lemac | Combinatòria |
dc.contributor.group | Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
dc.identifier.doi | 10.1016/j.endm.2015.06.064 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::05 Combinatorics::05C Graph theory |
dc.subject.ams | Classificació AMS::05 Combinatorics |
dc.rights.access | Open Access |
local.identifier.drac | 17503967 |
dc.description.version | Postprint (author's final draft) |
local.citation.author | Fiol, M. |
local.citation.publicationName | Electronic notes in discrete mathematics |
local.citation.volume | 49 |
local.citation.startingPage | 457 |
local.citation.endingPage | 463 |
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