简介:Thispaperstudiesrestrictedfaultdiameterofthen-dimensionalhypercubenetworksQn(n≥2).ItisshownthatforarbitrarytwoverticesxandywiththedistancedinQnandanysetFwithatmost2n-3verticesinQn-{x,y},ifFcontainsneitherofneighbor-setsofxandyinQn,thenthedistancebetweenxandyinQn-FisgivenbyD(Qn-F;x,y){=1,for=1;≤d+4,for2≤d≤n-2,n≥4;≤n+1,ford=n-1,n≥3;=n,ford=n.Furthermore,theupperboundsaretight.Asanimmediatelyconsequence,Qncantolerateupto2n-3verticesfailuresandremaindiameter4ifn=3andn+2ifn≥4providedthatforeachvertexxinQn,alltheneighborsofxdonotfailatthesametime.ThisimprovesEsfahanian'sresult.
简介:Inthispaper,wefocusonthevertex-fault-tolerantcyclesembeddingonenhancedhypercube,whichisanattractivevariantofhypercubeandisobtainedbyaddingsomecomplementaryedgesfromhypercube.LetFvbethesetoffaultyverticesinthen-dimensionalenhancedhypercubeQn,k(1≤k≤n-1).When|Fv|=2,weshowedthatQn,k-Fvcontainsafault-freecycleofeveryevenlengthfrom4to2n-4wheren(n≥3)andfchavethesameparity;andcontainsafault-freecycleofeveryevenlengthfrom4to2n-4,simultaneously,containsacycleofeveryoddlengthfromn—fc+2to2n-3wheren(≥3)andfchavethedifferentparity.Furthermore,when|Fv|=fv≤n-2,weproofthatthereexiststhelongestfault-freecycle,whichisofevenlength2n-2fvwhethern(n>3)andfehavethesameparityornot;andthereexiststhelongestfault-freecycle,whichisofoddlength2n-2fv-1inQn,k—Fvwheren(≥3)andfchavethedifferentparity.
简介:Inthispaper,theproblemoffault-tolerantroutingsinfault-tolerantnetworksisconsidered.Aroutinginanetworkassignstoeachorderedpairofnodesafixedpath.Allcommunicationamongnodesmustgoonthisrouting.Wheneitheranodeoralinkinafault-tolerantnetwork{ails,thecommunicationfromonenodetoanotherusingthisfaultyelementmustbesentviaoneormoreintermediatenodesalongasequenceofpathsdeterminedbythisrouting.Animportantandpracticalproblemishowtochoosearoutinginthenetworksuchthatintermediatenodestoensurecommunicationaresmallforanyfault-set,LetCdbeadirectedcycleoforderd.Inthispaper.Theauthor{irstdiscussesconnectivityofCartesianproductdigraphs,thenprovesthattheCartesianproductdigraphCd1×Cd2×…×Cdn(di≥2,1≤i≤n)hasaroutingsuchthatatmostoneintermediatenodeisneededtoensuretransmissionofmessagesamongallnon-faultynodessolongasthenumberoffaultsislessthann,ThisisageneralizationofDolevetal'sresultforthen-dimensionalcuhe.
简介:ThispaperconsidersthereliablecontroldesignforT-Sfuzzysystemswithprobabilisticactuatorsfaultsandrandomtime-varyingdelays.Thefaultsofeachactuatoroccursrandomlyanditsfailureratesaregovernedbyasetofunrelatedrandomvariablessatisfyingcertainprobabilisticdistribution.Intermsoftheprobabilisticfailuresofeachactuatorandtime-varyingrandomdelays,newfaultmodelisproposed.Basedonthenewfuzzymodel,reliablecontrollerisdesignedandsufficientconditionsfortheexponentiallymeansquarestability(EMSS)ofT-SfuzzysystemsarederivedbyusingLyapunovfunctionalmethodandlinearmatrixinequality(LMI)technique.Itshouldbenotedthattheobtainedcriteriadependonnotonlythesizeofthedelay,butalsotheprobabilitydistributionofit.Finally,anumericalexampleisgiventoshowtheeffectivenessoftheproposedmethod.