The generalized connectivity of the line graph and the total graph for the complete bipartite graph

摘要

The generalized k-connectivity κk(G) of a graph G, introduced by Hager (1985), is a natural generalization of the concept of connectivity κ(G), which is just for k=2. This parameter is often used to measure the capability of a network G to connect any k vertices in G. The line graph and the total graph are usually seen as important models for interconnection networks. In this paper, we determine the generalized 3-(edge-)connectivity of the line graph and the total graphs of the complete bipartite graph and discuss the bound for generalized 3-connectivity of the total graphs.