Paper Info
Title
Quasi-centers and radius related to some iterated line digraphs, proofs of several conjectures on de Bruijn and Kautz graphs.
Abstract
Bond (1987) and Bond et al. (1987), conjectured that a quasi-center in an undirected de Bruijn graph UB(d,D) has cardinality at least d−1, and that a quasi-center in an undirected Kautz graph UK(d,D) has cardinality at least d. They proved that for d≥3, the radii of UB(d,D) and UK(d,D) are both equals to D, and conjectured also that the radii of UB(2,D) and UK(2,D) are respectively D−1 and D. In this paper we give results in a more general context which validate these conjectures (excepting that asserting that the radius of UB(2,D) is D−1), and give simplified proofs of the cited results.
Year
DOI
Venue
2016
10.1016/j.dam.2015.08.025
Discrete Applied Mathematics
Keywords
Field
DocType
Quasi-center,Radius,Walk,de Bruijn graph,Kautz graph
Discrete mathematics,Graph,Combinatorics,Kautz graph,Cardinality,Radius,De Bruijn graph,Mathematical proof,De Bruijn sequence,Iterated function,Mathematics
Journal
Volume
Issue
ISSN
202
C
0166-218X
Citations 
PageRank 
References 
1
0.35
1
Authors
1
Name
Order
Citations
PageRank
Nicolas Lichiardopol111.02