2010
DOI: 10.1002/jgt.20458
|View full text |Cite
|
Sign up to set email alerts
|

The geometry oft‐spreads ink‐walk‐regular graphs

Abstract: 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 we comp… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1

Citation Types

0
2
0

Year Published

2022
2022
2023
2023

Publication Types

Select...
1
1

Relationship

0
2

Authors

Journals

citations
Cited by 2 publications
(2 citation statements)
references
References 14 publications
(17 reference statements)
0
2
0
Order By: Relevance
“…Next, we extend a result by Dalfó, Fiol, and Garriga [16] by showing that every antipodal distance-regular graph with odd diameter is a tight (d − 1)-CH graph (see CH2).…”
Section: The Values Xmentioning
confidence: 52%
See 1 more Smart Citation
“…Next, we extend a result by Dalfó, Fiol, and Garriga [16] by showing that every antipodal distance-regular graph with odd diameter is a tight (d − 1)-CH graph (see CH2).…”
Section: The Values Xmentioning
confidence: 52%
“…Thus, the (d − 1)-independence number α d−1 coincides with the so-called the dclique number or d-spread number ω d . In this context, Dalfó, Fiol, and Garriga [16] proved the following result.…”
Section: Maximally Independent Setsmentioning
confidence: 86%