dc.contributor.author Dalfó Simó, Cristina dc.contributor.author Fiol Mora, Miquel Àngel dc.contributor.author Garriga Valle, Ernest dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV dc.date.accessioned 2008-11-11T13:22:51Z dc.date.available 2008-11-11T13:22:51Z dc.date.issued 2008-09 dc.identifier.uri http://hdl.handle.net/2117/2355 dc.description.abstract A graph is walk-regular if the number of cycles of length $\ell$ rooted at a given vertex is a constant through all the vertices. For a walk-regular graph $G$ with $d+1$ different eigenvalues and spectrally maximum diameter $D=d$, we study the geometry of its $d$-cliques, that is, the sets of vertices which are mutually at distance $d$. When these vertices are projected onto an eigenspace of its adjacency matrix, we show that they form a regular tetrahedron and we compute its parameters. Moreover, the results are generalized to the case of $k$-walk-regular graphs, a family which includes both walk-regular and distance-regular graphs, and their $t$-cliques or vertices at distance $t$ from each other. dc.format.extent 11 p. dc.language.iso eng dc.rights Attribution-NonCommercial-NoDerivs 2.5 Spain dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/2.5/es/ dc.subject.lcsh Graph theory dc.subject.other Walk-regular graphs dc.subject.other k-walk-regular graphs dc.subject.other Spectral regularity dc.subject.other Crossel local multiplicities of eigenvalues dc.title The geometry of t-cliques in k-walk-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.subject.ams Classificació AMS::05 Combinatorics::05C Graph theory dc.rights.access Open Access
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