On Designing and Reconfiguring k-Fault-Tolerant Tree Architectures
IEEE Transactions on Computers
Distributed fault-tolerant embeddings of rings in hypercubes
Journal of Parallel and Distributed Computing
Designing fault-tolerant systems using automorphisms
Journal of Parallel and Distributed Computing
Arrangement graphs: a class of generalized star graphs
Information Processing Letters
Fault-Tolerant Ring Embedding in de Bruijn Networks
IEEE Transactions on Computers
On the construction of fault-tolerant Cube-Connected Cycles networks
Journal of Parallel and Distributed Computing
Embedding and Reconfiguration of Binary Trees in Faulty Hypercubes
IEEE Transactions on Parallel and Distributed Systems
Embedding a ring in a hypercube with both faulty links and faulty nodes
Information Processing Letters
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Embedding of Cycles in Arrangement Graphs
IEEE Transactions on Computers
Fault-Tolerant Meshes and Hypercubes with Minimal Numbers of Spares
IEEE Transactions on Computers
Embedding of Rings and Meshes onto Faulty Hypercubes Using Free Dimensions
IEEE Transactions on Computers
Embedding Cube-Connected Cycles Graphs into Faulty Hypercubes
IEEE Transactions on Computers
Fault-Tolerant Embedding of Complete Binary Trees in Hypercubes
IEEE Transactions on Parallel and Distributed Systems
Fault-Tolerant de Bruijn and Shuffle-Exchange Networks
IEEE Transactions on Parallel and Distributed Systems
Fault-Tolerant Ring Embedding in Star Graphs
IPPS '96 Proceedings of the 10th International Parallel Processing Symposium
Longest Fault-Free Paths in Star Graphs with Edge Faults
IEEE Transactions on Computers
Cycle embedding in faulty hierarchical cubic networks
Proceedings of the 2002 ACM symposium on Applied computing
Fault-tolerant Hamiltonicity of twisted cubes
Journal of Parallel and Distributed Computing
Fault-tolerant hamiltonian laceability of hypercubes
Information Processing Letters
Embedding Hamiltonian Paths in Faulty Arrangement Graphs with the Backtracking Method
IEEE Transactions on Parallel and Distributed Systems
Fault-tolerant cycle embedding in the hypercube
Parallel Computing
Fault Hamiltonicity and Fault Hamiltonian Connectivity of the Arrangement Graphs
IEEE Transactions on Computers
Embedding k(n - k) edge-disjoint spanning trees in arrangement graphs
Journal of Parallel and Distributed Computing
Hyper hamiltonian laceability on edge fault star graph
Information Sciences: an International Journal
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
Optimal Path Embedding in Crossed Cubes
IEEE Transactions on Parallel and Distributed Systems
Many-to-Many Disjoint Path Covers in Hypercube-Like Interconnection Networks with Faulty Elements
IEEE Transactions on Parallel and Distributed Systems
Edge-fault-tolerant edge-bipancyclicity of hypercubes
Information Processing Letters
Optimal fault-tolerant embedding of paths in twisted cubes
Journal of Parallel and Distributed Computing
Panconnectivity and edge-fault-tolerant pancyclicity of augmented cubes
Parallel Computing
Fault-tolerant pancyclicity of augmented cubes
Information Processing Letters
Fault-free cycles in folded hypercubes with more faulty elements
Information Processing Letters
International Journal of Computer Mathematics
Fault-Tolerant Hamiltonicity of Augmented Cubes under the Conditional Fault Model
ICA3PP '09 Proceedings of the 9th International Conference on Algorithms and Architectures for Parallel Processing
Edge-fault-tolerant edge-bipancyclicity of hypercubes
Information Processing Letters
On embedding cycles into faulty twisted cubes
Information Sciences: an International Journal
Path embedding on folded hypercubes
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Conditional edge-fault Hamiltonicity of augmented cubes
Information Sciences: an International Journal
Hamiltonian property on binary recursive networks
FAW'07 Proceedings of the 1st annual international conference on Frontiers in algorithmics
Hamiltonicity of matching composition networks with conditional edge faults
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Pancyclicity and bipancyclicity of conditional faulty folded hypercubes
Information Sciences: an International Journal
Hamiltonian properties of twisted hypercube-like networks with more faulty elements
Theoretical Computer Science
A note on cycle embedding in hypercubes with faulty vertices
Information Processing Letters
ω-wide diameters of enhanced pyramid networks
Theoretical Computer Science
Note: Embedding two edge-disjoint Hamiltonian cycles into locally twisted cubes
Theoretical Computer Science
Conditional matching preclusion for the arrangement graphs
Theoretical Computer Science
Conditional fault tolerance of arrangement graphs
Information Processing Letters
Regular connected bipancyclic spanning subgraphs of hypercubes
Computers & Mathematics with Applications
Edge-bipancyclicity of star graphs with faulty elements
Theoretical Computer Science
Fault-Free pairwise independent hamiltonian paths on faulty hypercubes
ACSAC'06 Proceedings of the 11th Asia-Pacific conference on Advances in Computer Systems Architecture
Two conditions for reducing the maximal length of node-disjoint paths in hypercubes
Theoretical Computer Science
Mutually independent hamiltonian cycles of binary wrapped butterfly graphs
Mathematical and Computer Modelling: An International Journal
Hamiltonian connectivity of 2-tree-generated networks
Mathematical and Computer Modelling: An International Journal
Matching preclusion and conditional matching preclusion for regular interconnection networks
Discrete Applied Mathematics
Hamiltonicity and Pancyclicity of binary recursive networks
ISPA'07 Proceedings of the 5th international conference on Parallel and Distributed Processing and Applications
Panconnectivity of n-dimensional torus networks with faulty vertices and edges
Discrete Applied Mathematics
Independent spanning trees in crossed cubes
Information Sciences: an International Journal
Fault diagnosability of arrangement graphs
Information Sciences: an International Journal
Fault-tolerant cycle embedding in the faulty hypercubes
Information Sciences: an International Journal
Hamiltonian path embeddings in conditional faulty k-ary n-cubes
Information Sciences: an International Journal
Hi-index | 0.01 |
The arrangement graph An,k, which is a generalization of the star graph (n驴k = 1), presents more flexibility than the star graph in adjusting the major design parameters: number of nodes, degree, and diameter. Previously, the arrangement graph has proved Hamiltonian. In this paper, we further show that the arrangement graph remains Hamiltonian even if it is faulty. Let |Fe| and |Fv| denote the numbers of edge faults and vertex faults, respectively. We show that An,k is Hamiltonian when 1) (k = 2 and n驴k驴 4, or k驴 3 and $n-k\ge 4+\left\lceil {{\textstyle{k \over 2}}} \right\rceil$), and |Fe| 驴k(n驴k) 驴 2, or 2) k驴 2, $n-k\ge 2+\left\lceil {{\textstyle{k \over 2}}} \right\rceil,$ and |Fe| 驴k(n驴k驴 3) 驴 1, or 3) k驴 2, n驴k驴 3, and |Fe| 驴k, or 4) n驴k驴 3 and |Fv| 驴n驴 3, or 5) n驴k驴 3 and |Fv| + |Fe| 驴k. Besides, for An,k with n驴k = 2, we construct a cycle of length at least 1) ${\textstyle{{n!} \over {\left( {n-k} \right)!}}}-2$ if |Fe| 驴k驴 1, or 2) ${\textstyle{{n!} \over {\left( {n-k} \right)! }}}-\left| {F_v} \right|-2\left( {k-1} \right)$ if |Fv| 驴k驴 1, or 3) ${\textstyle{{n!} \over {\left( {n-k} \right)! }}}-\left| {F_v} \right|-2\left( {k-1} \right)$ if |Fe| 驴 + |Fv| 驴k驴 1, where ${\textstyle{{n!} \over {\left( {n-k} \right)!}}}$ is the number of nodes in An,k.