| The topological structure of the interconnection network is a graph.The commu-nication using networks with cycle topological structure costs low,but have wide range of applications,so the cycle embedding has always been a hot topic in graph theory and computer research fields.The cycle embedding problem deals with the existence of a cycle with a given length.The pancyclicity is an extension of the cycle embedding.The study of pancyclicity is to discuss the existence of a cycle with every length be-tween the girth and ?V(G)? for a given graph.Recently,with the extensive application of cloud computing technology,data center carrying more and more servers,the network has been expanded.To this end,the researchers proposed a variety of new network structures used to support a larger scale network.Data center network is one of them.In this paper,by combining mathematical induction and classification method,we give the the structural analysis and pancyclicity discussion for the k-dimensional data center network with n-port switches Dk,n.This thesis is organized as follows.Chapter 1 is an introduction part.We introduce some basic definitions and pre-liminaries of related to this thesis and gave a brief introduction on the background of pancyclicity of graphs.In Chapter 2,we give the definitions and some properties of the k-dimensional data center network with n-port switches Dk,n.In Chapter 3,we study the embedding properties of the k-dimensional data cen-ter network with n-port switches Dk,n.The characterization of the structure of the k-dimensional data center network with n-port switches Dk,n is given.We proved that when n ? 5,for any edge(u,v)of the complete subgraphs Kn of Dk,n,there is a cycle of every length from 3 to ? V(Dk,n)? in Dk,n passing though the edge(u,v).Further more we obtain the pancyclicity and vertex-pancyclicity of k-dimensional data center network with n-port switches Dk,n.In Chapter 4,the conditional diagnosability of symmetric graphs under the com-parison model is given. |
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