Fault-diameter of the star-connected cycles interconnection network

Let G be a graph with vertex connectivity k(G). An important measure of the fault tolerance of G is its fault-diameter d_f(G), which is defined as the maximum diameter resulting from the deletion of any set of nodes containing less than k(G) nodes. The robustness of G is often measured by comparing d_f(G) with the diameter of the fault-free G, namely d(G). In particular, a family of graphs G_n is dubbed strongly resilient if d_f(G _n)⩽d(G_n)+c, where c is a fixed constant independent of n. This paper derives the fault-diameter of the star-connected cycles (SCC) interconnection network. We show that the SCC_n graph is strongly resilient, exhibiting a fault-diameter of d_f(SCC₃)=d(SCC₃)+4, d_f(SCC₄)=d(SCC₄)+5, and d_f(SCC_n)=d(SCC_n)+1, for n⩾5