Paper Info
Title
The geometry of t-spreads in k-walk-regular graphs
Abstract
A graph is walk-regular if the number of closed walks of length ℓ rooted at a given vertex is a constant through all the vertices for all ℓ. 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 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-spreads or vertices at distance t from each other. © 2009 Wiley Periodicals, Inc. J Graph Theory 64:312–322, 2010
Year
DOI
Venue
2010
10.1002/jgt.v64:4
Journal of Graph Theory
Keywords
Field
DocType
closed walk,three-dimensional case,walk-regular graph,different eigenvalues,wiley periodicals,distance-regular graph,spectrally maximum diameter,inc. j graph theory,k-walk-regular graph,adjacency matrix,regular graph
Graph center,Wheel graph,Graph power,Geometry,Path graph,Topology,Discrete mathematics,Combinatorics,Neighbourhood (graph theory),Cycle graph,Independent set,Distance-regular graph,Mathematics
Journal
Volume
Issue
ISSN
64
4
0364-9024
Citations 
PageRank 
References 
0
0.34
8
Authors
3
Name
Order
Citations
PageRank
Cristina Dalfó1469.47
M. A. Fiol281687.28
E. Garriga316419.92