角色分配及域近角色分配問(wèn)題之若干開(kāi)放問(wèn)題的研究.pdf

1、河北工業(yè)大學(xué)碩士學(xué)位論文角色分配及域近角色分配問(wèn)題之若干開(kāi)放問(wèn)題的研究姓名：李航申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：何文杰20040601——一魚(yú)璺坌醒墨苧塹壘魚(yú)坌墼旦望圭董王翌墓旦望盟塹塞THERESEARCHOFSEVERALOPENPROBLEMSoNROLEASSIGNMENTSANDTHRESHOLDROLEASSIGNMENTSABSTRACTEverettandBorgattiintroducedtheconcept

2、：kroleassignmentofgraphIfGisagraphakroleassignmentisasurjectivefunctionmap—pingeachvertexintoapositiveintegerl，2一k，s6thatif∞andYhavethes3]Tfierole，thenthesetsofrolesassignedtotheirneighborsaretheSOATIeThisideamotivatedin

3、socialnetworktheory，whereonetrlestodefinesocialrolesSOthatiftwoindividualsgetthesa【ITlesocialrole，theyassociatewithpeopleofthesamesetsofroleLiShengandRobertsstudied2roleassignmentsontriangulatedgraphsTheyputstheopenquest

4、ions：whethera西vengraphiskroleassignableforthecasek237Westudy硼59raphandthegridgraphandthehoneycombrectanglartorusandhoneycombrhomble：torusaccordinglyThegraphwithk—roleassignmenthasmanyexquisitepropertywhidlresultsinthecon

5、finedapplicability，SORobertsintroducedthefollowconcept：k—thersholdcloseroleassignmentofgraphPmbertsandLiShengshowedthateverygraphofatleastkverticeiskthreshholdcloseassignablefork=l，2，3，4，5Weproveinthispaperthatalmostever

6、ygraphis7threshholdcloseassignableandofferaimpactfulmethodtodistinguishwhethelagraphis7threshholdcloseassignablewhichmaketheproblemmachin9readableWeresovletheprobleminsenseofprobability，whichhasthesignificancethatthemeth