Based On Folded Hypercube And Cycles Cell-breeding Network And Its Properties

Interconnection network is an important part of super computers,the structure and properties of interconnection network are important research project of the super computer.When you design and select a topological structure for an interconnection network,some indicators such as planarity,Hamiltonian,connectivity and diameter play an important role in analyzing the performance of interconnection network.In this paper,we discussed the general folded cube-connected cycles network,new interconnection network FQCC(n,k)and the folded cube-connected cycles n-tuples Cartesian product network,which obtains the following results:1.The main results of the general folded cube-connected cycles network is:FQCC(n)(n>2):In 2010,Haizhong Shi conjectured that:FQCC(n)(n>2)can be decomposed into union edge-disjoint a Hamiltonian cycle and a perfect match-ing.We proved the general folded cube-connected cycles network is Hamiltonian decomposition and gave the algorithrns.Also we proved the general folded cube-connected cycles network is the choral ring network.2.The main results which are about the new interconnection network FQCC(n,k)based on the folded cube-connected cycles network and cell-breeding graph mod-el for interconnection network,Haizhong Shi designed another new interconnection network which is FQCC(n,k)(n>1,k is not a negative integer).It is 3 regu-lar and each vertex in the folded cube-connected cycles network is replaced by the cycles of length 3,and the vertex in every cycle is located on the edge of the folded cube-connected cycles and connected to the vertex,we called the new net-work FQCC(n,1);in similar way each vertex in the folded cube-connected cycles network FQCC(n,1)is replaced by the cycles of length 3,then we called the new net-work FQCC(n,2),looping execution the above method k times,and then get the new network FQCC(n,1)(n>1,k is not a negative integer).It has(n?1).2n·3k vertices and(n+1)· 2n-1 · 3k?1 edges.In this paper,(1)we proved FQC(2,k)(k?0)is pla-nar and Hamiltonian,FQCC(2,0)is Hamilton-connected,FQCC(3,0)is Hamilton-laceable;(2)we proved that FQCC(n,k)(n ? 2,3,4,5,k = 1)and FQCC(n,k)(k ?2)are neither vertex-transitive,nor Cayley graph.3.Haizhong Shi designed an interconnection network-the folded cube-connected cycles n-tuples Cartesian product network FQCC(d1,d2,…,di,).In this paper,we gave some properties and diameter of FQCC(d1,d2,…,dn).