The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.09 - September (2001 vol.50)
pp: 960-971
ABSTRACT
<p><b>Abstract</b>—In this paper, we aim to embed longest fault-free paths in an <it>n</it>-dimensional star graph with edge faults. When <tmath>$n\geq6$</tmath> and there are <tmath>$n-3$</tmath> 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 <tmath>$n-1$</tmath>, <tmath>$n-3$</tmath> (edge faults) is maximal in the worst case. When <tmath>$n\geq6$</tmath> and there are <tmath>$n-4$</tmath> edge faults, a longest fault-free path can be embedded between two arbitrary distinct vertices. The situation of <tmath>$n<6$</tmath> is also discussed.</p>
INDEX TERMS
Bipartite graph, embedding, fault tolerance, Hamiltonicity, longest path, star graph.
CITATION
Sun-Yuan Hsieh, Gen-Huey Chen, Chin-Wen Ho, "Longest Fault-Free Paths in Star Graphs with Edge Faults", IEEE Transactions on Computers, vol.50, no. 9, pp. 960-971, September 2001, doi:10.1109/12.954510
18 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool