Abstract
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.
Original language | English |
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Pages (from-to) | 960-971 |
Number of pages | 12 |
Journal | IEEE Transactions on Computers |
Volume | 50 |
Issue number | 9 |
DOIs | |
State | Published - Sep 2001 |
Keywords
- Bipartite graph
- Embedding
- Fault tolerance
- Hamiltonicity
- Longest path
- Star graph