A family of Hamiltonian and Hamiltonian connected graphs with fault tolerance

Authors:
Y-Chuang Chen;Yong-Zen Huang;Lih-Hsing Hsu;Jimmy J. Tan
Affiliations:
Department of Information Management, Ming Hsin University of Science and Technology, Hsinchu, Taiwan 304;Chunghwa Telecom Co., Ltd., Taoyuan, Taiwan 326;Department of Computer Science and Information Engineering, Providence University, Taichung, Taiwan 433;Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan 300
Venue:
The Journal of Supercomputing
Year:
2010

Citing 19
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Abstract

Processor (vertex) faults and link (edge) faults may happen when a network is used, and it is meaningful to consider networks (graphs) with faulty processors and/or links. A k-regular Hamiltonian and Hamiltonian connected graph G is optimal fault-tolerant Hamiltonian and Hamiltonian connected if G remains Hamiltonian after removing at most k驴2 vertices and/or edges and remains Hamiltonian connected after removing at most k驴3 vertices and/or edges. In this paper, we investigate in constructing optimal fault-tolerant Hamiltonian and optimal fault-tolerant Hamiltonian connected graphs. Therefore, some of the generalized hypercubes, twisted-cubes, crossed-cubes, and Möbius cubes are optimal fault-tolerant Hamiltonian and optimal fault-tolerant Hamiltonian connected.