K_(1,1)-structure connectivity and K_(1,1)-substructure connectivity of torus networks

摘要

The connectivity of a network is directly related to its reliability and fault tolerability, hence an important indicator of the network's robustness. In this paper, we investigate the fault-tolerant capabilities of torus networks with respect to the K_(1,1)-structure connectivity and K_(1,1)-substructure connectivity. The K_(1,1)-structure connectivity of a graph G, denoted by κ(G; K_(1,1)), is the minimum cardinality of a set of connected subgraphs in G, whose deletion disconnects the graph G and every element in the set is isomorphic to K_(1,1). The K_(1,1)-substructure connectivity of a graph G, denoted by κ~s (G; K_(1,1)), is the minimum cardinality of a set of connected subgraphs in G, whose deletion disconnects the graph G and every element in the set is isomorphic to a connected subgraph of K_(1,1). In this paper, we will establish both the K_(1,1)-structure connectivity and K_(1,1)-substructure connectivity of torus networks.