The h-extra connectivity of the star graph Networks

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 (kappa(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: kappa(h)(S-n) = (h + 1)n - 4h + 2 for h = 3,4 and n >= 7.