Aiheeseen liittyvät konseptit
Isolatedpoint:ThepointinVthatisnotassociatedwithanyedgeinEiscalledtheisolatedpointofD.
Simplegraph:Agraphwithoutparalleledgesiscalledasimplegraph.
Completegraph:BetweenanytwoverticesUanduinthegraph,thereareexactlytwodirectededges(u,v),and(v,u),thenCallthedirectedgraphDacompletegraph.
Basicgraph:RemoveeachedgeofthedirectedgraphDtogetacorrespondingundirectedgraphG,whichiscalledthebasicgraphofD.CallDTheDirectionalgraphofg.
Stronglyconnectedgraph:GivenadirectedgraphG=(VE),andgivenanytwonodesuandvinthegraphG,ifthenodeuItismutuallyreachablewithnodev,thatis,thereisatleastonepaththatcanstartfromnodeuandendatnodev,andthereisatleastonepaththatcanstartfromnodevandendatnodeu,thenitissaidthatthereshouldbeThedigraphGisastronglyconnectedgraph.
Weaklyconnectedgraph:Ifatleastonepairofnodesdoesnotsatisfyone-wayconnectivity,butafterremovingtheedgedirection,itisaconnectedgraphfromthepointofviewofanundirectedgraph,thenDiscalledItisaweaklyconnectedgraph.
One-wayconnectedgraph:Ifeachpairofnodesisconnectedinatleastonedirection,thenDiscalledaone-wayconnectedgraph.
Stronglyconnectedcomponent:TheextremelystronglyconnectedsubgraphofthedirectedgraphGiscalledthestronglyconnectedcomponentofthedirectedgraph.
Directedpath:Thereisalwayssuchanindependentset5inacyclicdirectedgraphD,sothatanypointiny-Js",thereexistsH∈S,fromMto"Thereisadirectedpathwithalengthnotexceeding2.
Vierekkäinen matriisi
Lukuun ottamatta Forisolatevertices, mikä tahansa.Siksi AnyDirectedGraph, riippumatta siitä,.Esimerkiksi, jos Daren reunat seuraavasti:
(1,1), (1,2), (1,3), (1,4), (2,2), (2,3), (2,4), (3,3), (3, 4), (4,4),
MotThatwelistTheedgesofDaccordingTotedictionarySekvenssi, Buthereisnota, B, C, C, C, C, C,..., but1,2,3....
Mukana,.TämäSteDiredgraphadjacencyMatrix.
Ratkaisu
ForthSesortestPathProblemofAdirectedGraph, The EcalculationStepsarethesameasSolvingthShortestPathProblemOfanDirectedGraph.ThraindifferenceishattheshortestPathproblemofanundirectedgraphusesasingLelAbelingMethod.Thesingle-labelingmethodistoassignaright of waylabeltoeachpoin.Thedoublelabelingmethodistoassigntwolabelstoeachpoint: thepathandtherightofway.
Saavutettavuus
Foranundirectedgraph, ifitisconnected, thentheremustbeapathbetbetweenytwoverticesofit.Siksi tämän kautta tämän läpi.Ifthevertex "canreachu, niin sitoa.
Fordirectedgraphs, theesiticationisdifferent, becausethereisapathfromutov, joka ei.
OleteDiredirectedGraph, andu, v∈D, jos seisApathFromverTexuverTexv, sittenTiSAIDToTverTexvToverTexuisReachable.
TheconceptOfreachbilityHasnothingTodowithTheNumberandlengthOftHeVariousPathsFromutov.Lisäksi FortSakeOfcleteness, itSSTIPOULTTHATANYVERTEXTOIFSSS ISREACHEAVA.
EsteettömyysRelationshipbetwevenheverTicesOfiredgedGraph.Mukana, ITISREFLEXIVEAndTransiitiivien mukaan.Yleisesti ottaminen, saavutettavuus.