| Interconnection network is an important part of super computers.Its topo-logical structure refers to the very large scale in the computer system components(processor)connection mode.In fact,its topological structure is a graph.The struc-ture and properties of interconnection network are important research projects of the super computer.When you design and select a topological structure for an intercon-nection network,some indicators such as degree of vertex,Hamiltonian,connectivity and diameter play an important role in analyzing the performance of interconnection networkIn this paper,we discussed the k Herschel-Shi connected cycles networks HSCC(1,k)and the Cartesian product network HSCC(1,k)× Cn1 × Cn2×...× Cnq.Which obtains the following results1.The main results of the networks HSCC(1,k):Haizhong Shi designed an interconnection network the k Herschel-Shi connected cycles networks HSCC(1,k)And Haizhong Shi proposed the following conjecture 1:the networks HSCC(1,k)are Hamilton decomposable.In this paper,(1)We study the number of vertex and edge,and studied the regular and connectivity of H SCC(1,k).(2)We proved that the conjecture 1 is true when k=0 and k=1,namely HSCC(1,0)and HSCC(1,1)are Hamilton decomposable.(3)We study when k=0 and k=1,the pancyclicity and bipancyclicity of network HSCC(1,k)and its cycle factor2.The main results of the Cartesian product networks HSCC(1,k)× Cn1 × Cn2 ×...×Cnq.Haizhong Shi designed an interconnection network the Cartesian product network HSCC(1,k)× Cn1× Cn2 ×...×Cnq.And Haizhong Shi proposed the follow-ing conjecture 2:the cartesian product networks HSCC(1,k)× Cn1× Cn2×...× Cnq are Hamilton decomposable.Especially,2.1 when q = 1 and n1=2,the Carte-sian product networks HSCC(1,k)× K2 are decomposable into two edge-disjoint Hamilton cycles;2.2when q = 1 and n1=m,the Cartesian product networks HSCC(1,k)× Cm are decomposable into two edge-disjoint Hamilton cycles and a perfect matching.In this paper,(1)We give some properties of this kind of network-s,and discusses some properties of the Cartesian product network HSCC(1,k)×K2 and HSCC(1,k)× Cm when q=1,n1=2 and q=1,n1=m,respective-ly.(2)We prove that the conjecture 2.1 is true when k=0 and k=1.And we prove that the conjecture 2.2 is true when k=0 and m=3.(3)We study the pan-cyclicity,bipancyclicity and cycle factor of network HSCC(1,k)× K2 when k=0 and k=1.(4)We study the pancyclicity,bipancyclicity and cycle factor of network HSCC(1,0)× C3 when k=0. |
