某些图类的Randi指标研究

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1、中国科学技术大学硕士学位论文某些图类的Randi指标研究姓名：宁文杰申请学位级别：硕士专业：应用数学指导教师：徐俊明2011-05-06ÁãØ´#,Æ,3¯õ+Ñk2A^5,CAcSuЩ×.Ù¥,'uãRandi´cI4¯KïÄ®²uФãØ¥ïÄ+.Randi´cI´«©zÆÿÀI,ùINõzÆ5k;éX.5,B.Bolloba´sÚErd¨osqrùVgí22ÂRandi´cI.Randi´cI4¯KïÄ´4ãØ;.A^.ùØ©ÌïÄ,ãaRandi´cêe.¿

2、Ñ4ã.31Ü©¥,·Äk0ãØuÐ{¤µ9~^âVg;,,2ÑRandi´cIVg,µ,ÌïįKÚ¤J.1Ü©,Äk·ïÄ(n,n+2)ãRandi´cI4.(n,n+2)ã´º:ên,>ên+2ã.·éùaãÑÙRandi´cIe.,¿xùe.(n,n+2)ã.Ùg,·ïÄ(n,n+r−1)ã¥aãRandi´cI4.ùaã´3¹kn−kº:,r−1l<Ýã,¥!^k+1´{üëÏã,Ù¥r≥2,k≥0.·éùaãÑÙRandi´cI;e..

3、1nÜ©,·o(©¤ó,¿Ñ?ÚïįK.'c:Randi´cIØ(n,n+2)ãl<Ýã.iAbstractBeingaboomingdiscipline,graphtheoryhasbeendevelopingrapidlyinrecentyearsbecauseofitswideapplicationsinvariousfields.TheresearchofRandi´cindiceshasbecomeoneofthemostimportanttopicingraphtheory.R

4、andi´cindexisanimportantchemicaltopologicalindexwhichhasacloserelationshipwithmanychemicalproperties.Afterwards,B.Bolloba´sandErd¨osgeneralizedittogeneralRandi´cindex.TheresearchonRandi´cindexitselfisatypicalapplicationofextremalgraphtheory.Thisthesism

5、ainlystudiessharplowerboundsoftheRandi´cindexofcertainfamiliesofgraphs.InPart1,weintroducethedevelopingbackgroundandsomeconceptsofgraphtheoryfirst.Afterthat,wepresentthethedefinitionandthebackgroundofRandi´cindex,themainprojectnowbeingstudiedandtheachiev

6、ement.InPart2,westudytheextremevalueoftheRandi´cindexof(n,n+2)-graphsfirst.Agraphiscalleda(n,n+2)-graphifithasnverticesandn+2edges.WegivesharplowerboundsontheRandi´cindexof(n,n+2)-graphs.Next,westudytheextremevalueoftheRandi´cindexofacertainfamilyofgrap

7、hsin(n,n+r−1)-graphs.Thesegraphsarethosesimpleandconnectedonesobtainedbyaddingapathoflengthk+1toacycleinacactuswithn−kverticesandr−1cycles,wherer≥2,k≥0.WegivesharplowerboundsontheRandi´cindexofthisclassofgraphs.Atlast,weconcludeourresearchinthispaperan

8、dproposesomequestionsthatareworthyoffurtherin-depthconsideration.Keywords:Randi´cindex,core,(n,n+2)-graphs,cactus,cycle.iii中国科学技术大学学位论文原创性声明本人声明所呈交的学位论文,是本人在导师指导下进行研究工作所取得的成果.除已特别加以标注和致谢的地方外,论文中不包含任何他人已经发表或撰写过的研究成果.与我一同工作的同志对本研究所做的贡献均已在