圖的鄰域參數(shù)研究.pdf

1、’Z10372：學位論文圖的鄰域參數(shù)研究馬永剛指導教師王志平教授申請學位級別理學碩士專業(yè)名稱應用數(shù)學學位授予單位大連海事大學2007年3月英文摘要AResearchonNeighborParametersofGraphsAbstractIntheprocessofdesigningandmaintainingtransportationcomputerorcommunicationnetworksthestability(vulnera

2、bility)ofthemisanimportantperformancecriterionTherefore，oneofthebasicideastodesignnetworksisthattheydonoteasilygetdisruptedunderexternalattackandtheyareeasilyreconstructediftheydeallygetdisruptedAnetworksystemcanbemodele

3、dbyaconnectedgraphinwhichverticesrepresentmodulesandedgesrepresentsomespecialconnectionbetweenthemodules，thenwecansolvetheproblemthroughthegraphtheoryUnderthemathematicalmodelofnetwoks，peoplebegantoputforwardsomeparamete

4、rstomeasnrethestabilityofnetworksAtthebeginning，vertex—connectivityandedgeconnectivityaretwoparametersoftenusedforitButthetwoparametershavesomedeficiencies，becausetheydonotthinkofthesurvival—subgraphafterremovingtheverti

5、cesoredgeshordertoovercomethedeficiencies，peoplehaveintroducedsomenewparameters，suchastoughness，scatteringnumberintcgaty，tenacityinthepastdecadeAlloftheseparametersaremorereasonablethanvertexconnectivityandedge—connectiv

6、ity，becausetheycallmeasurenotonlytheamountofworkdonetodamagethenetworkbutalsohowbadlythenetworkisdamagedIn1990，Cozzeusintroducedtheideaofmodelingaspynetworkbyagraphwhoseverticesrepresenttheagentsandwhoseedgesrepresentlin

7、esofcommunicationClearly，ifaspyisdiscoveredorarrested，theespionageagencycannolongertrustanyoftbespieswi山whomheorshewasindircctcommunicationandsothebetrayedagentsbecomeeffectivelyuselesstothenetworkasawholeItisobviousthat

8、wecannotmeasurethestabilityofspynetworkusingtheaboveparametersWiththebackgroundstatedabove，peopleintroducedsomenewparameters，suchasvertexneighborconnectivity，edgenei。ghborconneetivity，vertexneighborintegrityedge—neighbor

9、integrity，vertexneighborscatteringnumberedgeneighborscatteringnumberButtheseneighborparametershavesomedeficienciestomeasurethestabilityofsomenetworksThemaincontentsofthiSthesisareshowedasfollows：(1)Weintroducethebackgrol