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Longest fault-free paths in star graphs with edge faults

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3 Author(s)
Sun-Yuan Hsieh ; Dept. of Comput. Sci. & Inf. Eng., Nat. Chi Nan Univ., Taiwan, China ; Gen-Huey Chen ; Chin-Wen Ho

In this paper, we aim to embed longest fault-free paths in an n-dimensional star graph with edge faults. When n⩾6 and there are n-3 edge faults, a longest fault-free path can be embedded between two arbitrary distinct vertices, exclusive of two exceptions in which at most two vertices are excluded. Since the star graph is regular of degree n-1, n-3 (edge faults) is maximal in the worst case. When n⩾6 and there are n-4 edge faults, a longest fault-free path can be embedded between two arbitrary distinct vertices. The situation of n<6 is also discussed

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Computers, IEEE Transactions on  (Volume:50 ,  Issue: 9 )