Journal ArticleDOI
Embedding Hamiltonian paths in faulty arrangement graphs with the backtracking method
Ray-Shang Lo,Gen-Huey Chen +1 more
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To overcome the difficulty arising from random selection of the two end vertices, a new embedding method, based on a backtracking technique, is proposed and can tolerate more edge faults than Hsieh et al.Abstract:
The arrangement graph, denoted by A/sub n,k/, is a generalization of the star graph. A recent work by S.Y. Hsieh et al. (1999) showed that when n-k/spl ges/4 and k=2 or n-k/spl ges/4+[k/2] and k/spl ges/3, A/sub n,k/ with k(n-k)-2 random edge faults, can embed a Hamiltonian cycle. In this paper, we generalize Hsieh et al. work by embedding a Hamiltonian path between arbitrary two distinct vertices of the same A/sub n,k/. To overcome the difficulty arising from random selection of the two end vertices, a new embedding method, based on a backtracking technique, is proposed. Our results can tolerate more edge faults than Hsieh et al. results as k/spl ges/7 and 7/spl les/n-k/spl les/3+[k/2], although embedding a Hamiltonian path between arbitrary two distinct vertices is more difficult than embedding a Hamiltonian cycle.read more
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Journal ArticleDOI
Optimal path embedding in crossed cubes
TL;DR: It is proved that paths of all lengths between [(n+1)/2] and 2/sup n/-1 can be embedded between any two distinct nodes with a dilation of 1 in the n-dimensional crossed cube.
Journal ArticleDOI
Survey on path and cycle embedding in some networks
Jun-Ming Xu,Meijie Ma +1 more
TL;DR: A survey of the results related to pancyclicity and panconnectivity for the hypercube and some hypercube-like networks can be found in this article, where the authors also give a survey of related work for the non-hypercube case.
Journal IssueDOI
Panconnectivity, fault-tolerant hamiltonicity and hamiltonian-connectivity in alternating group graphs
TL;DR: In this paper, the authors showed that all alternating group graphs are pan-connected, that is, every two vertices x and y in the graph are connected by a path of length k for each k satisfying dlx, yr ≤ k ≤ vVv - 1, where d lx, y denotes the distance between X and y, and vvv is the number of vertices in the network.
Journal ArticleDOI
Hamiltonian circuit and linear array embeddings in faulty k-ary n-cubes
TL;DR: This paper proves that, for two arbitrary nodes, there exists a hamiltonian path connecting these two nodes in a wounded k-ary n-cube, and shows that the degrees of fault-tolerance 2n-3 and 2 n-2 respectively are optimal in the worst case.
Journal ArticleDOI
Hamiltonicity of the Hierarchical Cubic Network
Jung-Sheng Fu,Gen-Huey Chen +1 more
TL;DR: It is concluded that the hierarchical cubic network is superior to the hypercube in hamilton- icity, and the results can be applied to the hierarchical folded-hypercube network as well.
References
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Proceedings Article
A Group Theoretic Model for Symmetric Interconnection Networks.
TL;DR: The Cayley graph model as discussed by the authors is a formal group-theoretic model for designing, analyzing, and improving such networks, which enables the authors to design networks based on representations of finite groups.
Journal ArticleDOI
A group-theoretic model for symmetric interconnection networks
TL;DR: The Cayley graph model as mentioned in this paper is a formal group-theoretic model for designing, analyzing, and improving such networks, which enables the authors to design networks based on representations of finite groups.