关于图的优美、奇优美、奇优雅标号的研究-数学·运筹学与控制论专业论文.docxVIP

PAGE PAGE 1 Contents 独创性声明 i English Abstract ii Chinese Abstract iv HYPERLINK \l _TOC_250022 Chapter 1 Preliminaries 1 HYPERLINK \l _TOC_250021 Notations and Terminologies 1 HYPERLINK \l _TOC_250020 Some Particular Graphs 2 HYPERLINK \l _TOC_250019 Graceful Labellings of Graphs 3 HYPERLINK \l _TOC_250018 Results on Graceful Graphs 6 HYPERLINK \l _TOC_250017 Odd-graceful Labellings of Graphs 9 De?nitions and Conjectures 9 HYPERLINK \l _TOC_250016 Results on Odd-graceful Graphs 11 HYPERLINK \l _TOC_250015 Odd-elegant Labellings of Graphs 12 HYPERLINK \l _TOC_250014 Main Results 13 HYPERLINK \l _TOC_250013 Chapter 2 Graceful Labellings of Graphs 15 Graph Decompositions and Graceful Tree Conjecture 15 HYPERLINK \l _TOC_250012 0-Rotatable Tree Problem 18 HYPERLINK \l _TOC_250011 2.2.1 Some Results on 0-rotatable Trees 19 HYPERLINK \l _TOC_250010 Chapter 3 Odd-graceful Labellings of Graphs 26 HYPERLINK \l _TOC_250009 Constructing Odd-graceful Trees 26 HYPERLINK \l _TOC_250008 Odd-gracefulness of Spider Trees 33 HYPERLINK \l _TOC_250007 Odd-gracefulness of Lobster Trees 34 HYPERLINK \l _TOC_250006 Odd-gracefulness of Symmetric Trees 41 西 北 师 范 大 学 2 0 1 2 届 硕 士 学 位 论 文 HYPERLINK \l _TOC_250005 Chapter 4 Odd-elegant Labellings of Graphs 51 Odd-elegant Labellings of Lobsters and Trees With Smaller Diameters . 51 HYPERLINK \l _TOC_250004 Odd-elegant Labellings of Spiders 57 HYPERLINK \l _TOC_250003 Constructing Odd-elegant Graphs 62 HYPERLINK \l _TOC_250002 References 65 HYPERLINK \l _TOC_250001 Appendix 1 Published and Submitted Papers During Graduate Study Period 70 HYPERLINK \l _TOC_250000 Appendix 2 Acknowledgements 72 List of Figures (a) A graceful labelling of McGee graph; (b) a graceful labelling of Petersen graph; (c) a graceful labelling of Thomsen graph. 4 (a) A 0-rotatable tree; (b) a graph that cannot be gracefully labeled. 4 A strongly graceful tree with a perfect matching. This tree is also a lobster. 5 (a