The Super Connectedness And Restricted Connectivity Of Kronecker Product Graphs Of Paths,Cycles And Cycles

Since interconnection networks can be modeled by graphs,people always use connectedness parameters to measure the reliability of networks.The main drawback of using the classic vertex-connectivity to measure the reliability of networks is that it only considers the disconnectedness of the network,but not the properties of the components.In order to study the more refined connectedness parameters,researchers proposed all kinds of conditional connectivities,such as the super vertex-connectivity,restricted vertex-connectivity,cyclic vertex-connectivity,and so on.Based on known results of the connectedness of Kronecker product graphs,in this paper,we mainly study the super vertex-connectedness and restricted vertex-connectivity of Kronecker product graphs of paths,cycles and cycles.This paper is divided into three chapters.In Chapter 1,we introduce the research background,basic concepts and main results in this paper.In Chapter 2,we mainly study the super vertex-connectedness of Kronecker product graphs of the paths,cycles and cycles.We prove the following results:if integer m?4 and odd integer n? 3,then Pm × Cn is super vertex-connected;if integer m?5 and odd integer n? 3,then Cm×Cn is super vertex-connected.In Chapter 3,we obtain the restricted vertex-connectivity of Kronecker product graphs of paths,cycles and cycles.The main results are as follows:if integer m?4 and odd integer n? 5,then ?1(Pm × Cn)=?'(Pm × Cn)=4;if integer m?5 and odd integer n?5,then ?1(Cm × Cn)=?'(Cm × Cn)=6.