Fault-tolerant multiprocessor and VLSI-based system communication architectures
Fault-tolerant computing: theory and techniques; Vol. 2
The Hamiltonian property of generalized de Bruijn digraphs
Journal of Combinatorial Theory Series B
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 Hamiltonian property of linear functions
Operations Research Letters
The hamiltonian property of the consecutive-3 digraph
Mathematical and Computer Modelling: An International Journal
Note: Hamiltonicity of large generalized de Bruijn cycles
Discrete Applied Mathematics
| Hi-index | 0.98 |
A consecutive-d digraph with n nodes is a digraph whose nodes are labeled by the residues modulo n and a link from node i to node j exists iff j=qi+r,qi+r+1,...,qi+r+d-1 (mod n) where q and r are given. Many computer networks and multiprocessor systems use consecutive-d digraphs as their interconnection networks. A digraph is called Hamiltonian if it contains a spanning circuit. The Hamiltonian property provides the capability of configuring the interconnection network as a linear array, which is the configuration with broadcast practical significance of either n - 1 or n nodes in the presence of a single faulty node or link. Characterization of Hamiltonian consecutive-1 digraph has been previously given. In this paper, we prove that for gcd(n, q) 1 the consecutive-d digraph is Hamiltonian iff d = gcd(n, q); and for gcd(n, q) = 1 it is Hamiltonian if d = 5.