Some New Results Of The Wheel Networks And Bubble-sort Star Networks

Interconnection network is an important part of super computers. The designand capability analysis of the interconnection networks’topology structure deter-mine the efectiveness of parallel computer. The diameter and average distance of agraph are two important parameter for measuring the efciency of interconnectionnetworks. The distance domination number is a signifcant index for evaluating theperformance of network, and one of the central issues in evaluating an intercon-nection network is to study its hamiltonian. In this paper, we consider the wheelnetworks and the bubble-sort star networks obtain the following results:1. We proposed one varitey conjectures to show the structure of wheel network.Conjectures as follows: For any integer n4, Wheel network Wnis a union of i edge-disjoint hamiltonian cycles and2(n i)2perfect matchings, where1≤i≤(n1).We prove that conjectures are true for n=4,5,6and1≤i≤3.2. The diameter and the upper bound average distance of n-dimensional wheelnetwork are investigated and determine the value of diameter as well as the boundfor the upper bound average distance.3. The bounds of domination number, the distance2-domination number anddistance3-domination number of n-dimensional Bubble-sort star network are inves-tigated. And above the bounds are improved for some low dimensional Bubble-sortstar networks.4. The signed edge domination numbers of some Interconnection Networks areinvestigated in this paper. We obtain the bounds of signed edge domination numberof which for diferent dimensional.