scholarly journals A particular Hamiltonian cycle on middle levels in the De Bruijn digraph

2012 ◽  
Vol 312 (3) ◽  
pp. 608-613 ◽  
Author(s):  
Kramer Alpar-Vajk
Keyword(s):  
Hamiltonian Cycle ◽  
De Bruijn ◽  
De Bruijn Digraph

scholarly journals Isomorphisms of the De Bruijn digraph and free-space optical networks

Networks ◽  
2002 ◽  
Vol 40 (3) ◽  
pp. 155-164 ◽  
Author(s):  
D. Coudert ◽  
A. Ferreira ◽  
S. Perennes
Keyword(s):  
Optical Networks ◽  
Free Space ◽  
Free Space Optical ◽  
De Bruijn ◽  
De Bruijn Digraph ◽  
Free Space Optical Networks

New bounds on the decycling number of generalized de Bruijn digraphs

2017 ◽  
Vol 09 (05) ◽  
pp. 1750062
Author(s):  
Jyhmin Kuo ◽  
Hung-Lin Fu
Keyword(s):  
Feedback Vertex Set ◽  
Systematic Method ◽  
Minimum Cardinality ◽  
Disjoint Cycles ◽  
Decycling Number ◽  
Vertex Set ◽  
De Bruijn ◽  
De Bruijn Digraphs ◽  
Vertex Disjoint ◽  
De Bruijn Digraph

A set of vertices of a graph whose removal leaves an acyclic graph is referred as a decycling set, or a feedback vertex set, of the graph. The minimum cardinality of a decycling set of a graph [Formula: see text] is referred to as the decycling number of [Formula: see text]. For [Formula: see text], the generalized de Bruijn digraph [Formula: see text] is defined by congruence equations as follows: [Formula: see text] and [Formula: see text]. In this paper, we give a systematic method to find a decycling set of [Formula: see text] and give a new upper bound that improve the best known results. By counting the number of vertex-disjoint cycles with the idea of constrained necklaces, we obtain new lower bounds on the decycling number of generalized de Bruijn digraphs.

ON THE TWIN DOMINATION NUMBER IN GENERALIZED DE BRUIJN AND GENERALIZED KAUTZ DIGRAPHS

2010 ◽  
Vol 02 (02) ◽  
pp. 199-205 ◽  
Author(s):  
JYHMIN KUO
Keyword(s):  
Dominating Set ◽  
Domination Number ◽  
Kautz Digraphs ◽  
De Bruijn ◽  
Kautz Digraph ◽  
De Bruijn Digraph ◽  
Domination Numbers

Let V and A denote the vertex and edge sets of a digraph G. A set T ⊆V is a twin dominating set of G if for every vertex v ∈ V - T, there exist u, w ∈ T (possibly u = w) such that arcs (u, v), (v, w) ∈ A. The twin domination number γ*(G) of G is the cardinality of a minimum twin dominating set of G. In this note, we investigate the twin domination numbers of generalized de Bruijn digraph and generalized Kautz digraph. The bounds of twin domination number of special generalized Kautz digraphs are given.

THE DIAMETER AND HAMILTONIAN CYCLE OF THE GENERALIZED DE BRUIJN GRAPHS UGB(n, n(n+1))

1998 ◽  
Vol 09 (01) ◽  
pp. 13-23
Author(s):  
LUZ R. NOCHEFRANCA ◽  
POLLY W. SY
Keyword(s):  
Hamiltonian Cycle ◽  
De Bruijn Graph ◽  
De Bruijn Graphs ◽  
De Bruijn

In this paper, we will show that the diameter of the generalized De Bruijn graph UGB (n, n(n+1)) is 3 using an automorphism of the graph, and we will also give an algorithm to find a hamiltonian cycle of UGB (n, n(n+1)) for all integers n≥2.

scholarly journals Perfect matchings of a graph associated with a binary de Bruijn digraph

2010 ◽  
Vol 310 (22) ◽  
pp. 3241-3245 ◽  
Author(s):  
A. Kramer ◽  
F. Lastaria ◽  
N. Zagaglia Salvi
Keyword(s):  
Perfect Matchings ◽  
De Bruijn ◽  
De Bruijn Digraph

scholarly journals Particular cycles of a binary de Bruijn digraph

2010 ◽  
Vol 31 (2) ◽  
pp. 589-597 ◽  
Author(s):  
A. Kramer ◽  
N. Zagaglia Salvi
Keyword(s):  
De Bruijn ◽  
De Bruijn Digraph
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