简介:Itisprovedthatisa(Δ+1)-colorablegraph,soarethegraphsG×PnandC×Cn,wherePnandCnarerespectivelythepathandcyclewithnvertices,andΔthemaximumedgedegreeofthegraph.TheexactchromaticnumbersoftheproductgraphsPr1×Pr2×…×PrnandC3k×C2m1×C2m2×…×C2mnarealsopresented.Thusthetltalcoloringconjectureisprovedtobetrueformanyothergraphs.
简介:Inthispaper,buildingtogrid(B2G)andvehicletogrid(V2G)havebeendefinedwithclearandpracticalunderstanding.Bothofthemarenewgenerationtechnologieswhicharetheessentialpartofsmartcitylivingandcrowdenergyclustering.Firstly,anin-detailedoverviewhasbeenprovidedwithanintroductiontoB2GandV2Gfollowedbyahistoricaloverviewandtheoreticalanalysisinrespecttosmartcityplanning.Next,areviewisconductedoncurrentandprevioussmartlivingresearch,whichdealswithB2GandV2G.EfficientB2GandV2Gimplementationsinpracticalcasesthenhavebeendiscussed.Lastly,bothofthesetechnicalprospectshavebeenanalyzedincrowdenergydiagram.