Study On The Wide-diameter Of Double Loop Network

Double-loop networks(DLNs) are important topological structure of computer networksand communication systems, It has good properties such as regularity, optimal fault-toleranceand expandability, and have been widely used in local area networks and parallel processingarchitectures. Graph parameters such as connectivity and diameter have been studiedextensively due to their intrinsic importance in graph theory, combinatory and their relations tofault tolerance and transmission delay in communications networks.Since1970’s, much effort have been made to study the diameter, optimality, the averagediameter, double optimality, routing path, fault tolerance and the wide diameter of DLNs, andlots of contributions have been made.This paper is based on the mathematical theory. We design the simulation platform whichis studied on the Wide Diameter, the inherent laws about Wide Diameter Node and DiameterNode of directed double-loop networks. Main works in this thesis are summarized as follows:1.As for each double-loop network G(N;1,h),based on its definitions of diameter and widediameter,and by aid of routing for diameter and wide diameter in its equivalent L-tile,it isfounded that sum of diameter node and wide diameter node for each double-loop network isrespectively smaller than or equal to2,and that the diameter node must locate in the firstQuadrant, while the wide diameter node must locate on the x Axis or y Axis.2.A simulation platform is constructed. As for each double-loop network G(N;1,h), thesimulation platform is helpful for us to simulate the wide diameter node and the parallel pathsfor each double-loop network, the distribution regularities of wide diameter node are studied inthis thesis.3.As for double-loop network family G(N;1,2h N-1), by the increasing of step h, thevalue of its serial routing node has the characteristic of from small to big and then from big tosmall. Simulate the distribution diagram of diameter node and wide diameter node, it is foundedthat the value of diameter node and wide diameter node has the characheristic of fluctuatingdown, and that diameter node value is often bigger than wide diameter node value, and that theyboth reach biggest when step in the middle, and that as for one double-loop network, if thereexist two diameter nodes then there must exist two wide diameter nodes.