Structure Fault Tolerance of Fully Connected Cubic Networks

An interconnection network is usually modeled by a graph, and fault tolerance of the interconnection network is often measured by connectivity of the graph. Given a connected subgraph L of a graph G and non-negative integer t, the t-extra connectivity κt(G), the L-structure connectivity κ(G;L) and the t-extra L-structure connectivity κg(G;L) of G can provide new metrics to measure the fault tolerance of a network represented by G. Fully connected cubic networks FCn are a class of hierarchical networks which enjoy the strengths of a constant vertex degree and good expansibility. In this paper, we determine κt(FCn), κ(FCn;L) and κt(FCn;L) for t=1 and L∈{K1,1,K1,2,K1,3}. We also establish the edge versions λt(FCn), λ(FCn;L) and λt(FCn;L) for t=1 and L∈{K1,1,K1,2}.