| Títol: | The geometry of t-cliques in k-walk-regular graphs |
| Autor: | Dalfó Simó, Cristina
Fiol Mora, Miquel Àngel
Garriga Valle, Ernest |
| Altres autors/autores: | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV |
| Matèries: | Graph theory
Walk-regular graphs
k-walk-regular graphs
Spectral regularity
Crossel local multiplicities of eigenvalues
Grafs, Teoria de
Classificació 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
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