关于图一些标号的研究

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1、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iiiChapter1Preliminaries11.1BackgroundofGraphTheory...............11.2GraphLabellings......................21.3NotationsandTerminol

2、ogies................61.4MainResults........................8Chapter2GracefulLabellingsofGraphs112.1GracefulLabellingsofGraphs...............112.2DefinitionsofGracefulGraphs...............132.3SomeResultsonGracefulGraphs.............14Chapter3Odd-gracefulLabellingsofGraphs293.1SomeResul

3、tsofOdd-gracefulLabellings.........293.2DefinitionofOdd-gracefulLabelling............3153.3ReseachingResultsonOdd-gracefulGraphs.......32Chapter4FelicitousLabellingsofGraphs474.1FelicitousLabellingsofGraphs..............474.2DefinitionofFelicitousLabellings.............484.3SomeFelicitou

4、sGraphs..................49References65PublishedandSubmittedPapersDuringGraduateStudyPeriod71Acknowledgements73致致致谢谢谢75AbstractIn1966,inordertosettleRingel’sconjecture,Rosaintroducestheconceptofgraphlabellings:Agraphlabellingisamappingfromthevertexsetofagraphtoasetofintegers.Byvariousc

5、onstraintswehavemanytypesofgraphlabellings.Clearly,graphlabellingisanimportantbranchofgraphtheorysinceitcanbeappliedtoawideofscientificareas.However,therearemanynewproblemsyieldinginattackingfamousconjectures,suchasGracefulTreeConjecture,StronglyGracefulTreeConjecture,Odd-gracefulTreeCo

6、njecture,FelicitousTreeConjectureandsoon.Basedontheknownconclusionsandresultsongraphlabellings,myresearchingmainlyfocusonthefollowingaspects:ChapterOnedistributesasimpleintroductiontothedevelopmentofgraphtheoryandgraphlabellings.Basicterminologyandnotationofgraphtheoryaredefined,andthed

7、efinitions,conjecturesandsomeresultsofgraphlabellingsaregiven.ChapterTwoworksmainlyongracefullabellingofgraphs.Welistsomeresultsincurrentresearchinggracefullabellingofgraphs,andtrytoshowasummaryofstudyinggracefullabellingofgraphs.Weinvestigateparticulargracefullabellingsinordertofindso