博碩士論文 93241005 詳細資訊




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姓名 陳盈任(Ying-Ren Chen)  查詢紙本館藏   畢業系所 數學系
論文名稱 圖形分解與反魔圖
(Two Edge Labelings in Graphs :Graph Decomposition and Antimagic Labeling)
相關論文
★ 圖之均勻分解與有向圖之因子分解★ 加權圖之和、中位點及位移
★ 迴圈之冪圖的星林分解數★ 圖形的線性蔭度及星形蔭度
★ On n-good graphs★ A Note On Degree-Continuous Graphs
★ Status Sequences and Branch-Weight Sequences of Trees★ n-realizable Quadruple
★ 圖形的路徑分解,迴路分解和星形分解★ 星林圖的二分解與三分解
★ 2-decomposable, 3-decomposable multipaths and t-decomposable spiders★ The antimagic graph with a generalization
★ 圖的程度序列和狀態★ The 3-split of multipaths and multicycles with multiplicity 2
★ 圖形之分割與反魔標號
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摘要(中) 圖形分解是圖論中的一個非常重要課題。
因為它可以連接組合,代數和其他數學結構。
另一方面,圖分解的結果可以應用在編碼理論,實驗設計,計算機和通信網絡等領域。
反魔圖是圖形的一種標號。一般圖形標號是將圖形內的頂點
或邊給予對應的一個整數值的標號,
或兩者兼而有之。圖形標號推出在20世紀60年代中後期,
在這幾十年,圖形標號的研究論文已超過1500篇。
圖形標號結果已應用在計算機和通信網絡,應用統計學的研究,與一些設計科學等領域。
摘要(英) Graph decomposition is an important subject of graph theory.
Many combinatorial, algebraic, and other mathematical structures
are linked to decompositions of graphs,
which gives their study a great theoretical importance.
On the other hand, results on graph decompositions
can be applied in coding theory, design of experiments,
computer and communication networks, and other fields.
Nowadays, graph decomposition ranks the most prominent area
in graph theorey, even in combinatorics.
A graph is called an antimagic graph, if there exists an edge labeling which is an assignment of integers to the vertices
or edges, or both, subject to certain conditions. Graph labelings were first introduced in the late 1960s.
In the intervening years dozens of graph labelings techniques have been studied in over 1500 papers.
Graph labeling can be applied in computer and communication networks, applied statistics research,
and some design science other fields.
關鍵字(中) ★ 圖形分解
★ 反魔圖
★ 多重邊路徑
★ 蜘蛛分解
★ 球型上經緯線
★ 強乘績
關鍵字(英) ★ Decomposition
★ Antimagic
★ Multipaths
★ spider decomposition
★ globes
★ Strong product
論文目次 I Graph Decompositions ...........................1
1 Introduction to Graph Decompositions ............2
2 The 2-split of Multipaths and Multicycles with Multiplicity2 ...........................................7
2.1 Introduction to t-splits of graphs . . . . . . . . . . . . . . . . 7
2.2 The 2-split of multipaths and multicycles with multiplicity 2 ............... 8
3 The Spider Decomposition of Complete Bipartite Graphs
and Crowns............ 36
3.1Introduction . . . . . . . . . . . . . . .. . . . . . 36
3.2 Sl(2)-decomposition of the complete bipartite graph Kn;tl . . ........... 38
3.3 Sl(2)-decomposition of Cn;k . . . . . . . . . . . . . . . . . . . 45
II Antimagic graphs ............53
4 Introduction to antimagic graphs.......... 54
5 Strong product graphs............ 58
5.1 Introduction . . . . . . . . . . . . . . . . . . . . 58
5.2 Strong product graphs . . . . . . . . . . . . . . . . . . . . . . 60
6 Globes, Hemispheres and Mobius grids.... 68
6.1 Globes and Hemispheres . . . . . . . . . . . . . . . . . . . . . 68
6.2 Mobius grids . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Bibliography ..............90
參考文獻 [1] A. Rosa, On certain valuations of a graph, Theory of Graphs, Rome
(1966) 349-355
[2] B. Alspach, D. Dyes and D. L. Kreher, On isomorphic factorization of
circulant graphs, J. Combin. Des. 14 (2006) 406-414.
[3] B. W. Jackson, Some cycle decompositions of complete graphs, Journal
of Combinatorics, Information and System Sciences 13 (1988), 20{32.
[4] C. A. Parker, Complete bipartite graph path decompositions Ph. D. Dissertation,
Auburn University, Auburn, Alabama, 1998.
[5] C. Huang and A. Rosa, On the existence of balanced bipartite designs,
Utilitas Math. 4 (1973), 55{75.
[6] C. Huang, On the existence of balanced bipartite designs II, Discrete
Math 9 (1974), 147{159.
90
[7] C. Lin , J. J. Lin and Tay-woei Shyu, Isomorphic star decompositions of
multicrowns and the power of cycles, Ars Combin. 53 (1999), 249-256.
[8] C. Lin and T.-W. Shyu, A necessary and sucient condition for the star
decomposition of complete graphs, J. Graph Theory 23 (1996), 361{364.
[9] C. Vanden Eynden, Decomposition of complete bipartite graphs. Ars
Combin. 46 (1997), 287-296.
[10] D. De Caen and D. G. Ho man, Impossibility of decomposing the complete
graph on n points into n
指導教授 林強(Chiang Lin) 審核日期 2013-7-15
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