Some Properties Of M?bius Cube Networks And M?bius Cube-connected Cycles Networks

Interconnection network is an important part of super computers.Its topology structure refers to the very large scale in the computer system components(pro-cessor)connection mode,Interconnection network structure and properties is an important topic of the supercomputer research.In the process of design and selec-tion of interconnection network,Hamilton sex,ring embedded,connectivity,such as diameter index to analyze network performance played an important role.In this paper,we consider M?bius cube networks,the M?bius cube-connected cycles networks and the Cartesian product networks of the M?bius cube-connected cycles obtain the following results.1.The main results about M?bius cube networks:In 2010,Shi Haizhong pro-posed a conjecture:for any integer n = 2k,M?bius cube networks is a union of k edge-disjoint Hamiltonian cycles;for any integer n = 2k+1,M?bius cube networks is a union of k edge-disjoint Hamiltonian cycles and a perfect matching.we prove the conjecture is true for n = 3,4,5;M?bius cube networks is a union of 2 edge-disjoint Hamiltonian cycles and 2 perfect matchings for n = 6.2.The main results about M?bius cube-connected cycles networks:The concrete structure based on Shi Haizhong proposed a definition about M?bius cube-connected cycles networks.To prove MQCC(n)is to have n·2n vertices and 3n·2-1 reg-ular figure and the upper and.lower bounds of the diameter is given.The hamilton decomposition of MQCC(3)and MQCC(4).Finally use constructing method to prove the MQCC(n)is the hamilton decomposable.3.The main results about n product of M?bius cube-connected cycles network-s:According to the design of Shi Haizhong about cartesian product of 0-M?bius cube-connected cycles networks and 1-M?bius cube-connected cycles networks.This paper studies the network of the two vertices,regularity,vertex connectivity and edge connectivity,etc.We proved the Qnk can be embedded into the 0-M?bius cube-connected cycles networks and 1-M?bius cube-connected cycles networks.