关于图一些标号研究

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1、分类号密级UDC编号10736硕士学位论文关于图的一些标号的研究研究生姓名：张家娟指导教师姓名、职称：姚兵副教授专业名称：运筹学与控制论研究方向：图论及其应用二〇一三年五月OnSeveralGraphLabellingsJiajuanZhang西北师范大学研究生学位论文作者信息论文题目关于图的一些标号的研究姓名张家娟学号2010210800专业名称运筹学与控制论答辩日期2013.05.10联系电话E_mail通信地址(邮编)：备注：ContentsAbstracti摘摘摘要要要iiiChapter1Preliminari

2、es11.1BackgroundofGraphTheory...............11.2GraphLabellings......................21.3NotationsandTerminologies................61.4MainResults........................8Chapter2GracefulLabellingsofGraphs112.1GracefulLabellingsofGraphs...............112.2Definitio

3、nsofGracefulGraphs...............132.3SomeResultsonGracefulGraphs.............14Chapter3Odd-gracefulLabellingsofGraphs293.1SomeResultsofOdd-gracefulLabellings.........293.2DefinitionofOdd-gracefulLabelling............3153.3ReseachingResultsonOdd-gracefulGraphs....

4、...32Chapter4FelicitousLabellingsofGraphs474.1FelicitousLabellingsofGraphs..............474.2DefinitionofFelicitousLabellings.............484.3SomeFelicitousGraphs..................49References65PublishedandSubmittedPapersDuringGraduateStudyPeriod71Acknowledgement

5、s73致致致谢谢谢75AbstractIn1966,inordertosettleRingel’sconjecture,Rosaintroducestheconceptofgraphlabellings:Agraphlabellingisamappingfromthevertexsetofagraphtoasetofintegers.Byvariousconstraintswehavemanytypesofgraphlabellings.Clearly,graphlabellingisanimportantbrancho

6、fgraphtheorysinceitcanbeappliedtoawideofscientificareas.However,therearemanynewproblemsyieldinginattackingfamousconjectures,suchasGracefulTreeConjecture,StronglyGracefulTreeConjecture,Odd-gracefulTreeConjecture,FelicitousTreeConjectureandsoon.Basedontheknownconclu

7、sionsandresultsongraphlabellings,myresearchingmainlyfocusonthefollowingaspects:ChapterOnedistributesasimpleintroductiontothedevelopmentofgraphtheoryandgraphlabellings.Basicterminologyandnotationofgraphtheoryaredefined,andthedefinitions,conjecturesandsomeresultsofgr

8、aphlabellingsaregiven.ChapterTwoworksmainlyongracefullabellingofgraphs.Welistsomeresultsincurrentresearchinggracefullabellingofgraphs,andtrytoshowasummaryofstu