Abstract

Reliability analysis is important to the design of large multiprocessor systems. Connectivity, super connectivity and extra connectivity are important parameters to evaluate the reliability of multiprocessor systems. As a generalization of connectivity and super connectivity, extra connectivity has received much research attentions. The h-extra connectivity of the star graph (K h (S n )) for h = 1,2 have been obtained by Cheng et al for n ≥ 3, n ≥ 4, respectively. In this paper, we extend their results. The h-extra connectivity of the star graph for h = 3,4 is determined as follows: K h (S n ) = (h + 1)n — 4h + 2 for h = 3,4 and n > 7.

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