Connectivity of Imase and Itoh Digraphs
IEEE Transactions on Computers
Generalized de Bruijn digraphs
Networks
The Hamiltonian property of generalized de Bruijn digraphs
Journal of Combinatorial Theory Series B
On the numbers of spanning trees and Eulerian tours in generalized de Bruijn graphs
Discrete Mathematics
Counting closed walks in generalized de Bruijn graphs
Information Processing Letters
On the domination numbers of generalized de Bruijn digraphs and generalized Kautz digraphs
Information Processing Letters
On the k-tuple domination of de Bruijn and Kautz digraphs
Information Processing Letters
Absorbant of generalized de Bruijn digraphs
Information Processing Letters
Connectivity of Regular Directed Graphs with Small Diameters
IEEE Transactions on Computers
Design to Minimize Diameter on Building-Block Network
IEEE Transactions on Computers
A Design for Directed Graphs with Minimum Diameter
IEEE Transactions on Computers
The twin domination number in generalized de Bruijn digraphs
Information Processing Letters
On the k-tuple domination of generalized de Brujin and Kautz digraphs
Information Sciences: an International Journal
Topological Structure and Analysis of Interconnection Networks
Topological Structure and Analysis of Interconnection Networks
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Given a digraph (network) G=(V,A), a vertex u in G is said to out-dominate itself and all vertices v such that the arc (u,v)@?A; similarly, u in-dominates both itself and all vertices w such that the arc (w,u)@?A. A set D of vertices of G is a k-tuple twin dominating set if every vertex of G is out-dominated and in-dominated by at least k vertices in D, respectively. The k-tuple twin domination problem is to determine a minimum k-tuple twin dominating set for a digraph. In this paper we investigate the k-tuple twin domination problem in generalized de Bruijn networks G"B(n,d) and generalized Kautz G"K(n,d) networks when d divides n. We provide construction methods for constructing minimum k-tuple twin dominating sets in these networks. These results generalize previous results given by Araki [T. Araki, The k-tuple twin domination in de Bruijn and Kautz digraphs, Discrete Mathematics 308 (2008) 6406-6413] for de Bruijn and Kautz networks.