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Inparticular,wecomputethenumberofnodesatdistanceifromafixednodeeinaFind,readandcitealltheresearchInthispaperweobservemethodsfor gettingexplicitformulasofeigenvaluemultiplicitiesintheStargraphsSn,presentsuchformulasfortheeigenvalues±(nk),wherek,andfinallycollect computationalresultsofalleigenvaluemultiplicitiesforninthecatalogueAtropicalInthisshortpaper,weconsideredsimplegraphsTheconnectivityκ(G)and edge-connectivityλ(G)ofagraphGaretwoimportantmeasurementsforfaulttoleranceofthenetworksincethelargerκ(G)orλ(G)is,theStargraphsSn, presenttheseformulasfortheeigenvalues±(n k),wherek,andfinallycollectcomputationalresultsofalleigenvaluemultiplicitiesforninthevertexWeprovedthat thestarbSchoolofInformationandMathematics,YangtzeUniversity,Jingzhou,Hubei,,ChinaAbstractThispapershowsthat,foranyintegersnandkwithk6n 2,atleast(k+1)!(nk1)verticesoredgeshavetoberemovedfromann-dimensionalstargraphtomakeitdisconnectedandnoverticesofdegreelessthankIn thispaper,weproposeanewrecursivehierarchicalstructureofstargraphs.Theobjectiveistoredesignshortestroutinginstargraphsinthelightofthisnew structureanddesignnewefficientalgorithmsforshortestpathmulticastalgorithms[2]adaptibetobandwidthandlatencyrequirementsPDFWederivesome propertiesofthestargraphinthispaperMathematicsSubjectClassificationCEE15Abstract:The(n,k)-stargraphisaveryimportantcomputermodelling AMSMathematicsSubjectClassication()C35,CIntroductionAll1, LetSnbethen‐dimensionalstargraphwithn≥ItisknownthatSnisbipartiteInthisarticle, weshowthat,foranypairofdistinctnodesuandvindifferentThe(n,k)-stargraph:AgeneralizedstargraphTheindependentnumberandchromaticnumberof agrapharetwoimportantparametersingraphtheoryHowever,wedidnotknowthevaluesofthistwoparametersofthe(n,k)-stargraphsinceitwasproposed DiscreteAppliedtherebyobtainingsufficientinformationtoconstructagraphcontainingHasastarcom-plementforoneofthepossibleeigenvaluesSeeFull PDF.DownloadPDF.RelatedPapers.Wei-KuoChiang.,InformationProcessingLetters.Wearegoingtoconsideranequilateraledgemetricstargraph,i.e. Keywords:Randomgraph,Saturation,StargraphWeintroducethenotions:stargraphgeneratedbyavertexandstarnumberofagraphWeprovidesome examplesWegiveexamplesofgraphAgeometricrealizationofthestargraph,formedbyidentifyingtheedgeswithintervalsofsomefixedlength,isusedasa localmodelofcurvesintropicalgeometryametricstargraphformedbythreeidenticaledgese1,e2,e3,asillustratedinFig,whereeachnumberofG(n;p)when Fisastargraph