Conditional Connectivity And Maximal Local Connectivity Of Two Types Of Cayley Graphs

With the rapid development of information network,reliability of networks come into focus.If we use vertices to express processors and edges to express communication links,the underlying topology of a network can be modeled as a graph.Some classical concepts of graph theory,such as vertex connectivity and edge connectivity,have long been used to study the reliability of the network.In order to further study.A variety of connectivity concepts,such as conditional connectivity and maximal local connectivity,are proposed.Cayley network,as a regular,vertex-symmetric interconnect network,is more and more popular.It plays an important role in the design and analysis of the interconnect network.In this article.We study a kind of conditional vertex connectivity of Cayley graphs generated by wheel graphs and fault tolerant maximal local connectivity of Cayley graphs generated by 2-trees.In the first chapter.We give some of the basic concepts and symbols,and simply introduce the related research progress.In the second chapter.We first study the relationship between Cayley graphs generated by 2-trees and Cayley graphs generated by wheel graphs,then we study the properties of Cayley graphs generated by wheel graphs by the related properties of Cayley graphs generated by 2-trees,and then study the?~1and?~2for Cayley graphs generated by wheel graphs.In the third chapter.We study fault tolerant maximal local connectivity of Cayley graphs generated by 2-trees,and extend the one-to-one maximally local connectivity to one-to-many maximally local connectivity,then explore fault tolerant one-to-many maximal local connectivity of Cayley graphs generated by 2-trees,at last,we explore the fault tolerant maximal local connectivity of Cayley graphs generated by 2-trees under the condition that each vertex has at least three fault free adjacent vertices.