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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. Inform. Process. Lett. 112 (2012), no. 21, 844-847. [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- ence (LNCS) 3595 (2005) 671-679.
指導教授	林強	審核日期	2015-1-14
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