A Study Of Dodecahedron-Shi Connected Cycles Network And Its Cartesian Product Network

Interconnection network is an important part of the super computer,to a great extent,decides the performance of super computer.Its topological struc-ture refers to the very large scale in the computer system components(processor)connection mode.The structure and properties of interconnection network are im-portant research projects of the super computer.When you design and select a topology structure for an interconnection network,some indicators such as Hamil-tonian,pancyclicity,cycle factor,connectivity and diameter play an important role in analyzing the performance of interconnection network.On the basis of regular graph connected cycles network model and dodecahedron,professor Haizhong Shi designed a new dodecahedral-Shi connected cycles network for interconnect network DSCC(k)and cartesian product network DSCC(k)× Cn1 × Cn2 ×…× Cnq,and put forward the following conjecture,guess 1:k dodecahedral-Shi connected cycles network DSCC(k)is Hamilton decomposable.Guess2:cartesian product network DSCC(k)× Cn1 × Cn2 ×…× Cnq is Hamilton decomposable.In particular,when q=1,n1=2,DSCC(k)× K2 is the union of edge-disjoint two Hamiltonian cycles;When q=1,n1=m,DSCC(k)× Cm(m?3)is the union of edge-disjoint two Hamiltonian cycles and a perfect matching.In this paper,we discussed the dodecahedron-Shi connected cycles network DSCC(k),the cartesian product networks DSCC(k)× K2,DSCC(k)× Cm(m? 3)and DSCC(k)× Cn1 × Cn2 ×…× Cnq,which obtains the following results:1.The main results of the dodecahedral-Shi connected cycles networks DSCC(k):Haizhong Shi designed an interconnection network-DSCC(k).In this paper,(1)we proved that DSCC(k)is Hamilton decomposable,and on the basis of this conclu-sion,it proves two general hypotheses put forward by professor Haizhong Shi.(2)we give the pancyclicity of the DSCC(k),and proved the DSCC(k)is neither pan-cyclic nor bipancyclic.(3)we discussed the DSCC(k)of p-factor decomposition,it is proved that DSCC(k)of a certain number of turns of 2-factor for k=0,1 and k? 1.(4)we give some basic properties of the DSCC(k),and proved2.The main results of the cartesian product networks DSCC(k)× K2 and DSCC(k)× Cm(m? 3):According to the new networks DSCC(k)× K2 and DSCC(k)× Cm(m? 3)constructed by Haizhong Shi.In this paper,(1)we proved that DSCC(k)× K2 is Hamilton decomposable when k=0,1,2 and DSCC(k)×Cm(m? 3)is Hamilton decomposable When m=3,4 and k=0,1,2.(2)we proved the DSCC(k)× K2 is bipancyclic for k=0 and DSCC(k)× K2 is bipancyclic and DSCC(k)× Cm(m?3)is edge-bipancyclic.(3)we discussed the DSCC(k)× K2 and DSCC(k)× Cm(m?3)of p-factor decomposition,it is proved that DSCC(k)× K2 is 2-factor decomposable and DSCC(k)× Cm(m? 3)is 2-factor decomposable for k=0.772=3,4.(4)we given and proved some basic properties of DSCC(k)× K2 and DSCC(k)× Cm(m?3)3.The main results of the cartesian product networks DSCC(k)× Cn1 × Cn2 ×…×Cnq:Haizhong Shi designed an interconnection network DSCC(k)× Cn1 ×Cn2 ×…×Cnq.In this paper,(1)we proved that DSCC(k)× Cn1 × Cn2 ×…× Cnq is Hamilton decomposable for k=0,q=2,n1=n2=2.(2)we given and proved some basic properties of the DSCC(k)× Cn1 × Cn2 ×…× Cnq.