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dc.contributor | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV |
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dc.contributor | Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
dc.contributor.author | Dalfó Simó, Cristina |
dc.contributor.author | Fiol Mora, Miquel Àngel |
dc.contributor.author | Garriga Valle, Ernest |
dc.date | 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.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 2.5 Spain |
dc.rights | info:eu-repo/semantics/openAccess |
dc.rights | http://creativecommons.org/licenses/by-nc-nd/2.5/es/ |
dc.subject | Graph theory |
dc.subject | Walk-regular graphs |
dc.subject | k-walk-regular graphs |
dc.subject | Spectral regularity |
dc.subject | Crossel local multiplicities of eigenvalues |
dc.subject | Grafs, Teoria de |
dc.subject | Classificació AMS::05 Combinatorics::05C Graph theory |
dc.title | The geometry of t-cliques in k-walk-regular graphs |
dc.type | info:eu-repo/semantics/article |