Abstract
We derive the fault-diameter of the star graph using a combinatorial method, thereby resting the previously open question of finding the exact value for the fault diameter of the star graph. This method is based on counting the number of node-disjoint paths of optimal length between a given pair of nodes in the graph and distributing the faulty nodes among these paths in a worst-case fashion. The fault-diameter for the n-star graph is shown to be D n + 1 for n ⩾ 7, where D n is the diameter of the fault-free star graph.
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