Restricted And Structure Connectivity Of Several Networks

With the deepening of modern scientific research and the continuous progress of engineering technology,the application level and research depth of high performance computing(or supercomputing)has become an important symbol to measure the level of science and technology of a country.As an important means to achieve high performance computing,the development of supercomputer has become one of the key research fields in various countries.Because supercomputer is often a multiprocessor system with tens of thousands of processors,the design of the connection mode between processors becomes the key of developing supercomputer.Therefore,as the basic topology of multiprocessor system,the research of interconnection networks becomes an important topic.Because the topology structure of the interconnection networks directly determines the construction cost,bandwidth,delay,reliability and other characteristics of the corresponding multiprocessor systems,the evaluation of network performance has become a hot direction.Among them,reliability is the primary factor to measure the network performance.Among many parameters for evaluating network reliability,connectivity and its generalizations are particularly important.In this dissertation,we mainly evaluate the reliability of several widely studied interconnection networks from the perspective of connectivity.The main contents are as follows:(1)In order to generalize the condition that per dimension of hypercube can only take 0 or 1,Bhuyan and Agrawal proposed generalized hypercube.The topology structure of this network has good recursion.Moreover,it has excellent combinatorial properties,such as node-disjoint path,wide diameter and fault diameter.In order to further evaluate the reliability of this network topology,we study its h-restricted connectivity.We compare our results with the traditional connectivity in the summary part.In addition,we extend the previous works on the structure connectivity of the generalized hypercube.(2)As we know,one n-dimensional hypercube can be constructed by two(n-1)dimensional hypercubes.Motivated by it,the idea of replacing each vertex of some graph with hypercubes Qrs to construct new interconnection networks is proposed.In this dissertation,we define a class of graphs g which includes hierarchical cubic networks and complete cubic networks,and we obtain:for any graph G ∈ g,the h-restricted connectivity of G is 2h(r+1-h)(1 ≤h≤r-2).(3)Cayley graphs are widely studied network topologies.Based on the alternating group,Jwo et al.proposed the alternating group graphs.This network has good recursion and is superior to hypercube in pancyclicity and unicast.In this dissertation,we first try to generalize the previous results of h-restricted connectivity of alternating group graphs.We obtain that κ4(AG5)=24.Then,we study the(sub)structure connectivity of alternating group graphs and obtain:Finally,in the summary part,we compare and analyze the advantages of this parameter in evaluating the reliability of alternating group graphs.