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 Títol: The geometry of t-cliques in k-walk-regular graphs Autor: Dalfó Simó, CristinaFiol Mora, Miquel ÀngelGarriga Valle, Ernest Altres autors/autores: Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. COMBGRAF - Combinatòria, Teoria de Grafs i Aplicacions Matèries: Graph theoryWalk-regular graphsk-walk-regular graphsSpectral regularityCrossel local multiplicities of eigenvaluesGrafs, Teoria deClassificació AMS::05 Combinatorics::05C Graph theory Tipus de document: Article Descripció: 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. Altres identificadors i accés: http://hdl.handle.net/2117/2355 Disponible al dipòsit: E-prints UPC Comparteix:

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