Minimum neighborhood in a generalized cube

Authors:
Xiaofan Yang;Jianqiu Cao;Graham M. Megson;Jun Luo
Affiliations:
School of Computer and Information, Chongqing Jiaotong University, Chongqing 400074, P.R. China and College of Computer Science, Chongqing University, Chongqing 400044, P.R. China;School of Computer and Information, Chongqing Jiaotong University, Chongqing 400074, P.R. China;Department of Computer Science, School of Systems Engineering, University of Reading, P.O. Box 225, Whiteknights, Reading, Berkshire RG6 6AY, UK;College of Computer Science, Chongqing University, Chongqing 400044, P.R. China
Venue:
Information Processing Letters
Year:
2006

Citing 15
Cited 2

The Twisted N-Cube with Application to Multiprocessing

IEEE Transactions on Computers
The twisted cube topology for multiprocessors: a study in network asymmetry

Journal of Parallel and Distributed Computing
A new variation on hypercubes with smaller diameter

Information Processing Letters
On Diagnosability of Large Fault Sets in Regular Topology-Based Computer Systems

IEEE Transactions on Computers
Introduction to Parallel Processing: Algorithms and Architectures

Introduction to Parallel Processing: Algorithms and Architectures
The Möbius Cubes

IEEE Transactions on Computers
The Crossed Cube Architecture for Parallel Computation

IEEE Transactions on Parallel and Distributed Systems
Super-connectivity and super-edge-connectivity for some interconnection networks

Applied Mathematics and Computation
Diagnosability of regular systems

Journal of Algorithms
Maximum number of edges joining vertices on a cube

Information Processing Letters
Hamiltonian properties on the class of hypercube-like networks

Information Processing Letters - Devoted to the rapid publication of short contributions to information processing
The t/k-Diagnosability of the BC Graphs

IEEE Transactions on Computers
Fault-Hamiltonicity of Hypercube-Like Interconnection Networks

IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Papers - Volume 01
Maximum induced subgraph of a recursive circulant

Information Processing Letters
The diagnosability of the matching composition network under the comparison diagnosis model

IEEE Transactions on Computers

Hamiltonian properties of twisted hypercube-like networks with more faulty elements

Theoretical Computer Science
The spined cube: A new hypercube variant with smaller diameter

Information Processing Letters

Quantified Score

Hi-index	0.89

Visualization

Abstract

Generalized cubes are a subclass of hypercube-like networks, which include some hypercube variants as special cases. Let @q"G(k) denote the minimum number of nodes adjacent to a set of k vertices of a graph G. In this paper, we prove @q"G(k)=-12k^2+(2n-32)k-(n^2-2) for each n-dimensional generalized cube and each integer k satisfying n+2=