網(wǎng)絡拓撲結(jié)構設計中兩個問題的研究.pdf

1、中國科學技術大學碩士學位論文網(wǎng)絡拓撲結(jié)構設計中兩個問題的研究姓名：鄧志國申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：徐俊明200403012004年中國科學技術大學碩士學位論文4ABSTRACTThedissertationshowssomestudyOUthetopologicalstructureofnetworks】tcontainstwopartsasfollows：ThefirstpartdiscussesabouttheDia

2、metersofAlteredGraphs。Forgivenpositiveintegerstandd(≥2)，LetF(≠，d)andP(t，奶denotetheminimumdiameterofagraphobtainedbyaddingtextraedgestoagraphandapathwithdiameterd，respectivelyandf(t，d)denotethemaximumdiameterofagraphobtai

3、nedafterdeletingtedgesfromagraphwithdiameterdItisknownthatP(1d)=嘲ford≥2，p(2，d)=f丁di]ford≥3，P(a，d)=f丁d21ford≥5，and，ingeneral，害一1≤P(t，d)百d4了13fort，d≥4Inthispart，weestablishF(t，f(t，d))≤d5f(t，F(xiàn)(t，d))andprove『矗1sF(t，d)=P(t，d)

4、sl酉d2J3Moreover，F(xiàn)(t，d)5l宅量j1ifdisenoughlargeParticularlywederivetheexatvaluesP(t，(2k一1)p1)1)=2kforanypositiveintegerk，and『告]≤P(t，d)曼『擊]1fort=4ort=5andd≥4ThesecondpartisaboutWideDiameterofMSbiusCubesSupposethatGisa∥一conne

5、ctedgraphByMenger’stheoremthereexistwinternallydisjointpathsbetweenanytwodistinctverticesinG、thesmallestnumberfforwhichthere&rewhlternallydisjointpathsoflengthatmost￡betweenanytwoverticesinGiscalledthewidediameterofG，den

6、otedby比(G)TheM6biuscubeisavariantofthehypercubeandhasbetterperformancethanthehypercubewiththesamenumberoflinksandprocessorsThispapershowsthatthewidedialneterofttleMSbiuscubeisatmostf等112，aboutonehalfofthesa_inedimensiona