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Fault-tolerant ring embedding in faulty arrangement graphs

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2 Author(s)
Sun-Yuan Hsieh ; Dept. of Comput. Sci. & Inf. Eng., Nat. Taiwan Univ., Taipei ; Gen-Huey Chen

The arrangement graph An,k, which is a generalization of the star graph (n-t=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 proven 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-k⩾4, or k⩾3 and n-k⩾4+[k/2]), and |Fe|⩽k(n-k-2)-1, or (2) k⩾2, n-k⩾2+[k/2], and |F e|⩽k(n-k-3)-1, or (3) k⩾2, n-k⩾3, and |F3 |⩽k

Published in:

Parallel and Distributed Systems, 1997. Proceedings., 1997 International Conference on

Date of Conference:

10-13 Dec 1997