博碩士論文 101221017 詳細資訊




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姓名 黃衍勝(Yan-sheng Huang)  查詢紙本館藏   畢業系所 數學系
論文名稱
(The antimagic graph with a generalization)
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摘要(中) 反魔術圖是圖形的一種標號,當我們找到一種標號方式使得圖形的所有點之和都不相同時,我們稱這種圖形是反魔術圖。
在這篇論文中,第一章我們討論反魔術圖的一些基本定義,第二章證明路徑(path)與星林(star forest)的聯集,在每一分量(component)的邊數都大於等於3的情況下是反魔術圖,第三章討論更廣義的反魔術性質,也證明了環路(cycle),完全圖(complete),輪子(wheel),風箏(kite)都是廣義的反魔術圖。
摘要(英) A graph G is called an antimagic graph if exists an edge labeling with labels 1,2,⋯,|E(G)| such that all vertex sums are distinct.
In this paper, Section 1 is the introduction of antimagic graph. In Section 2, we prove that the union of a path and some stars is antimagic. Section 3 is the introduction of antimagic with a generalization, and we prove that cycles, complete graphs, wheels and kites are R-antimagic.
關鍵字(中) ★ 圖論
★ 反魔術
關鍵字(英)
論文目次 Contents

Abstract (in Chinese) i
Abstract (in English) ii
誌謝 iii
Contents iv
1 Introduction 1
2 Antimagicness of disconnected graphs 4
3 A generalization of antimagic graph 8
References 20
參考文獻 [1]N. Alon, G. Kaplan, A. Lev, Y. Roditty and R. Yuster, Dense graphs are
anti-magic, J. Graph Theory 47 (4) (2004) 297-309.
[2] P.D. Chawathe and V. Krishna, Antimagic labeling of complete m-ary
trees, Number theory and discrete mathematics (Chandigarh, 2000), 77-80,
Trends Math., Birkhuser, Basel, 2002.
[3] D.W. Cranston, Regular bipartite graphs are antimagic, J. Graph Theory
60 (2009), 173-182.
[4] J. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. 19
(DS6) (2012) (the Fifteenth edition).
[5] N. Harts eld and G. Ringel, Pearls in Graph Theory, Academic Press,
Boston, 1990.
[6] D. Hefetz, Antimagic graphs via the combinatorial nullstellensatz, J. Graph
Theory 50 (2005) 263-272.
[7] G. Kaplan, A. Lev and Y. Roditty, On zero-sum partitions and anti-magic
trees, Discrete Math., 309 (2009) 2010-2014.
[8] M.J. Lee, C. Lin and W.H. Tsai, On antimagic labeling for power of cycles.
Ars Combin. 98 (2011), 161-165.
[9] J.L. Shang, C. Lin and S.C. Liaw, On the antimagic labeling of star forests,
to appear.
[10] R. Sliva, Antimagic labeling graphs with a regular dominating subgraph.
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[11] M. Sonntag, Antimagic vertex-labelling of hypergraphs, Discrete Math. 247
(2002) 187- 199.
[12] T.M. Wang and C. Hsiao, On anti-magic labeling for graph products, Dis-
crete Math. 308 (2008) 3624-3633.
[13] T.M. Wang and M.J. Liu, Deming Some classes of disconnected antimagic
graphs and their joins, Wuhan Univ. J. Nat. Sci. 17 (2012), no. 3, 195-199.
[14] T. Wang, M.J. Liu and M.D. Li, A class of antimagic join graphs, Acta
Math. Sin. 29 (2013), no. 5, 1019-1026.
[15] T.M. Wang, Toroidal grids are anti-magic, Lecture Notes in Computer Sci-
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指導教授 林強 審核日期 2015-1-14
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