欢迎来到天天文库
浏览记录
ID:34579751
大小:1.19 MB
页数:85页
时间:2019-03-08
《图特征值与度序列》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、万方数据EigenvaluesandDegreeSequencesofGraphsByGuangjunZhangUndertheGuidanceofProfessorXiao-DongZhangAppliedMathematicsSpecialityGraphTheoryanditsApplicationsDepartmentofMathematicsSupportedbyNationalScienceFoudationofChinagrants10531070万方数据万方数据万方数据_______________________________________________
2、__________________________________________᤺⌕_________________________________________________________________________________________Ḅᱯᑡ᤺⌕ḄDᳮEFᔠᦪẆHḄI⌕7⚪,ᨵḼI⌕ḄᳮMNOP▭)ᵨRS,ᙠTUᓄ、XYZ&、[]、[^_ᨵḼI⌕ᙢ.6ᦻa⌕bcRiemanndeḄLaplacianYUḄfᦣᓄhḄLaplaciani▣ḄDirichletᱯ、kᩗḄᱯOmnZopqr.☢tuẆH.✌ᐜ,ᡃy
3、ẆHRiemanndeḄFaber-Krahnzᳮᙠfᦣ{
4、}Ḅ~,ᱯẆHzᑡ0zḄᓫᙌOzᑡḄᙌ_ᐹᨵᨬḄhDirichletᱯḄ.ẆH⊤Faber-Krahnzᳮz▲ᑴḄ~ᡂ.ᐸ,ᡃyẆHkᩗḄᱯ,ᱯẆHzᑡOᩗIḄkᩗḄp-LaplacianᱯOkᩗᓫᙌḄᱯ.ẆH⊤ᙠzᑡOᩗIḄkᩗ_ᐹᨵᨬᜧp-LaplacianDḄEhḄ,Pᐵ;¡ᙠzᑡOᩗIḄkᩗᓫᙌ_ᐹᨵᨬᜧ¢£DḄ¤zᑡḄᓫᙌ_ᐹᨵᨬᜧ¢£DḄᨵ¥¦Ḅ§ᡫ©᪀.ᨬ«,ᡃyẆHmnZop,¬hropឋ¯Ḅ°±~.²³ឋ¯ᩭ<µnZop,
5、¶nZopḄh³6¯ᱯ.ᐵ¸¹:hDirichletᱯp-LaplacianDkᩗmnZI万方数据ᜧᦻEigenvaluesandDegreeSequencesofGraphsABSTRACTThetheoryofgraphspectralwiththeoreticsignificanceandstrongapplicationbackgroundisanimportantareaincombinatorialmathematicsandplaysanimportantroleinquantumchemistry,computerscience,c
6、ommunicationnetworkandinformationscience.ThisthesisisdevotedtodiscussingthefirstDirichleteigenvalueofLaplacianmatrix,whichcanbeseenasthediscreteanalogofthecontinuousLaplace-Beltrami-operatoronmanifolds,theeigenvaluesofweightedgraphsandquasi-randombipartitegraphs.First,westudythediscreteanalo
7、gofFaber-Krahninequalityonmanifolds.Especially,westudythegraphswiththeminimumfirstDirichleteigenvalueamongallunicyclicgraphswithagivendegreesequenceandwithgivennumberofboundaryvertices,andamongthebicyclicgraphswithgivendegreesequence.TheresultsshowthattheFaber-Krahntypetheoremfortheabovegrap
8、hclassesholds.Second,weinvestigatetheeigenvaluesofweightedgraphs.Especially,westudythep-Laplacianeigenvaluesofweightedtreeswithagivendegreesequenceandapositiveweightsetandtheadjacenteigenvaluesofweightedunicyclicgraphswithagivendegreesequenceandapo
此文档下载收益归作者所有