K1, 1-structure connectivity and K1, 1-substructure connectivity of torus networks
Yali Lv, Yulong Xu · 2017
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 K1, 1-structure connectivity and K1,1-substructure connectivity. The K1,1-structure connectivity of a graph G, denoted by κ(G; K1,1), 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 K1,1. The K1,1-substructure connectivity of a graph G, denoted by κs(G; K1,1), 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 K1,1. In this paper, we will establish both the K1,1-structure connectivity and K1,1-substructure connectivity of torus networks.