12960.r一致超圖的譜

1、分類號01576r一致超圖的譜密級0ntheSpectralradiiofruniformhypergraphs論學(xué)研又編號科專究方運(yùn)籌學(xué)與控制論圖論及其應(yīng)用湖南師范大學(xué)學(xué)位評定委員會辦公室二零一六年四月r一致超圖的譜02AbstractThespectraofgraphtheoryisaveryimportantresearchareainalgebragraphtheory，whichstudyonalgericproperties

2、andapplicationsaboutassociatedmatricesofgraphS，suchaStheAdjacencymatrb【，theIncidencematri)【，theLapida卜ianmatri)【，thesinlesslapidarianmatri)【andsoonInthispapergraphswhich盯ediscussedaresimpleconnectedHypergraphisageneraliz

3、ationofthegraph，thespec—tralofhypergraphhalSattracttherese甜cherofgr印h’sattentionBefore2005，theresearchonspectralofhypergraphbasedonthematr恢，buthypergraphandmatrb【isnotonetoonecorrespondence，thematri)【isuncertainnom2004，l

4、iqunQiofHongKongdefineSthetensorspectral，gongqingZhangandliqunQidepictsomepropertiesofthetensorspectral，the8ef6rreseachingonthetensorspectrallayatheoreticaJfoundationaJld行鋤eworkTherefore，Wewillinvestigatethestudyofthespe

5、ctr出radiusofhypergr印hwithgivennumberofbranchingverticesandruniformline盯hypergr印hTllispaperisdividedintothreepartsandthemainstructureofthearticleisasfbllowsInchapter1：weintroducethefundarnentalconceptsandpropertiesofgraph

6、sandhypergraplls，aJlsothedomesticandforeignreseaurchingsituationsInchapter2：Inthischapter，westudythespectralradiiof南uniformhppergraphsontheoperationofsplittingaVertexandsomee)(tremalprobleInsofspectralradiiof3uniformsupe

7、rtreesW宅provethat兀七is3uniformsupertreeswiththemaximumspectralradiiamongall3一uniformsupertreeswith佗verticesand七pendentedgesw宅alsoshowthat礙is3uniformsupertreeswiththema)【imumspectralradiiamongaU3一uniformsupertreeswith佗vert