Some Domination Parameters Of Pancake Network And Its Circle Decomposition

Network is an important part of supercomputers.Its topology refers to the connection mode of components(processors)in very large-scale computer systems.The structure and nature of interconnection networks are important topics in su-percomputer research.In the process of designing and selecting the interconnection network,Hamilton character,circle embedding,connectivity,diameter and other indicators play an important role in analyzing network performance.The pancake network is a typical supercomputer interconnection network de-signed by the group theory model of the interconnection net.work.The pancake network has many excellent properties.However,it has certain defects in some aspects,that is,the degree of node increases with the scale.Large and rapid in-crease,in order to improve this shortcoming,Hai-zhong Shi proposed a hierarchical ring group theory model of the interconnection network and designed a layered ring pancake network.This paper discusses the topology of the pancake network and the hierarchi-cal pa.ncake network and the four types of control numbers of the pancake network(point control number,symbol control number,inverse symbol control number,mi-nus control number)and gives the specific calculation method.The main results as follows:1.Hai-zhong Shi proposed the conjecture of the pancake network PNn and proved that it was established in the low-dimensional case.That is,when n is even,PNn can be decomposed into n-2/2 Hamilton circles and a perfect match;when n is odd,PNn can be decomposed into n-1/2 Hamilton circles.When n=2,3,4,the guess is true,given in this article There are two loop decompositions of PN5.2.Hai-zhong Shi constructed a new network PNn × Ck1 × Ck2...×Ckq(where Cki is a ki long circle and ki?3),and a conjecture is given to the network and proved to be true in low-dimensional situations.,that is,when n is odd,PNn ×Ck1 × Ck2...× Ckq Decomposed into n-1/2+q a sum of Hamilton circles;when n is even,PNn × CK1×Ck2...×Ckq can be decomposed into sides that don' t pay n-2/2+q A Hamilton circle and a perfectly matched sum.When n=2,3,4,the guess is true,and in this article we give PN5×C3 A loop decomposition.3.In this paper,the specific values give the four types of control numbers(point control number,symbol control number,anti-symbol control number,and decrement control number)of the pancake network PNn are given and their calcu-lation methods are given.PNn point control,?(PNn)(n-1)!PNn's signed control numberWhen n is odd,?s(PNn)=(n-1)!;When n is even,?s(PNn)=2(n-1)!;Anti-symbol control number of PNn When n is odd,??s(PNn)=(n-1)!;When n is even,??s(PNn)=0;PNn minus control,?-1(PNn)=(n-1)!.