Vulnerability issues of star graphs, alternating group graphs and split-stars: strength and toughness

Akers et al. (Proceedings of the International Conference on Parallel Processing, 1987, pp. 393–400) proposed an interconnection topology, the star graph, as an alternative to the popular n-cube. Jwo et al. (Networks 23 (1993) 315–326) studied the alternating group graph An. Cheng et al. (Super connectivity of star graphs, alternating group graphs and split-stars, Ars Combin. 59 (2001) 107–116) proposed the split-star as an alternative to the star graph which can be viewed as a companion graph of An. All of these graphs have maximal connectivity. In this paper, we study these interconnection topologies using advanced measures of vulnerability, namely, strength and toughness. Moreover, we show that with respect to toughness, a star graph is no better than an n-cube, whereas the alternating group graph and split-star are tougher than both of these graphs. ? 2002 Elsevier Science B.V. All rights reserved.