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The geometry of t-spreads in k-walk-regular graphs

Author
Dalfo, C.; Fiol, M.; Garriga, E.
Type of activity
Journal article
Journal
Journal of graph theory
Date of publication
2010-08
Volume
64
Number
4
First page
312
Last page
322
DOI
https://doi.org/10.1002/jgt.20458 Open in new window
Repository
http://hdl.handle.net/2117/8043 Open in new window
Abstract
A graph is walk-regular if the number of closed walks of length rooted at a given vertex is a constant through all the vertices for all . For a walk-regular graph G with d+1 different eigenvalues and spectrally maximum diameter D=d, we study the geometry of its d-spreads, 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 simplex (or tetrahedron in a three-dimensional case) and ...
Keywords
Walk-regular graphs, eigenvalue multiplicities, local spectrum
Group of research
COMBGRAPH - Combinatorics, Graph Theory and Applications

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