Structure And Strong Menger Connectivity Of Some Hypercube-like Networks

Except the first chapter-introduction,this paper mainly includes two topics:structure connected and strongly Menger connected.The connectivity of a graph G is an important parameter in graph theory,and is also one of the most important indicator in evaluating the reliability and faulty tolerance of a network.Chapter 2 mainly dealing with the structure connectedκ（G;S）and the substructure connectedκ^s（G;S）of augmented cubes.The following results have been proved:n≥5,In particular,κ^s（AQ_n;C₄）=n.In Chapter 3 mainly dealing with the strongly Menger connected,and we prove that:balanced hypercube BH_n（n≥4）is 2n-2-fault-tolerant strongly Menger connected;balanced hypercube BH_n（n≥2）is 2n-4-conditional fault-tolerant strongly Menger connected;balanced hypercube BH_n（n≥2）is 2n-2-conditional edge-fault-tolerant strongly Menger connected.In Chapter 4 mainly dealing with the strongly Menger edge-connected,and we prove that:enhanced hypercube Q_n,k（n≥3,2≤k≤n-1）is 2n-2-conditional edge-fault-tolerant strongly Menger connected.