Fault Tolerance And Diagnosis Of Variant Networks Based On Hypercube

Graph theory is one of the important means and tools for dealing with discrete problems in mathematics,such as structure and optimization problems in computer in-terconnection networks.Connectivity is one of the most basic concepts in graph theory,and it is also the basis of network design and analysis.The connectivity of the corre-sponding graph can be used to measure the reliability of the network.In the network of real-time supercomputer systems,structure connectivity,conditional connectivity and conditional diagnosability are several graph theory concepts related to connectivity Faults of components and wires in large-scale interconnection networks are inevitable When point or edge faults occur in networks,corresponding graph theory parameters al-so change.Whether subnetworks retain the nature of the original network is a problem that researchers have been concerned aboutIn this paper,we mainly study the properties and performance parameters of some variant networks of Hypercubes and combinatorial networks,as well as the relation-ship between them.The first chapter is a summary of the background,progress and results of the issues involved in this paper.In the second chapter,by characterizing the structure of graphs,we study the structure connectivity of twisted cube networks,and obtain the star(K1,r)structure connectivity(r=3,4)and path(Pk)structure connec-tivity(1?k?n)of twisted cube networks Hn and their substructure connectivity,respectively.Secondly,in the third chapter,with the help of the fault-tolerant Hamil-tonian property of restricted HL-graphs,the fractional matching preclusion problem of restricted HL-graphs is studied by extending the matching problem of graphs.The frac-tional matching preclusion number and strong fractional matching preclusion number of n-dimensional restricted HL-graphs are obtained,and the structural characteristics of the optimal strong fractional preclusion set of all 4-dimensional restricted HL-graphs are characterized.In Chapter 4 and Chapter 5,we first study the g-extra connectivity of twisted hypercubes and hierarchical cubic networks,and then give the g-extra condition diagnosability of twisted hypercubes and hierarchical cubic networks under PMC mod-el and the g-extra condition diagnosability of twisted hypercubes and hierarchical cubic networks under MM*model.In addition,we also put forward some questions that need further study.