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On t-cliques in k-walk-regular graphs

Author
Dalfo, C.; Fiol, M.; Garriga, E.
Type of activity
Journal article
Journal
Electronic notes in discrete mathematics
Date of publication
2009-08
Volume
34
First page
579
Last page
584
DOI
https://doi.org/10.1016/j.endm.2009.07.096 Open in new window
Repository
http://hdl.handle.net/2117/8041 Open in new window
Abstract
A graph is walk-regular if the number of cycles of length 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 result...
Citation
Dalfo, C.; Fiol, M. A.; Garriga, E. On t-cliques in k-walk-regular graphs. "Electronic notes in discrete mathematics", Agost 2009, vol. 34, p. 579-584.
Keywords
Clique, Distance-regular graphs, Spectrum, k-Walk-regular graphs
Group of research
COMBGRAPH - Combinatorics, Graph Theory and Applications

Participants