Longest Fault-Free Paths in Star Graphs with Edge Faults

• Authors: Sun-Yuan Hsieh;Gen-Huey Chen;Chin-Wen Ho
• Venue: IEEE Transactions on Computers
• Year: 2001

In this paper, we aim to embed longest fault-free paths in an n-dimensional star graph with edge faults. When $n\geq6$ 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 $n\geq6$ and there are $n-4$ edge faults, a longest fault-free path can be embedded between two arbitrary distinct vertices. The situation of $n