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論文名稱 Title |
在整數上標號的半魔圖 The Z-Semimagic of Some Graphs |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
35 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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口試日期 Date of Exam |
2011-07-28 |
繳交日期 Date of Submission |
2011-08-22 |
關鍵字 Keywords |
指標集、指標、半魔圖、半魔圖指標、標號 index set, index, semimagic index, Z-semimagic, edge labeling |
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統計 Statistics |
本論文已被瀏覽 5728 次,被下載 1613 次 The thesis/dissertation has been browsed 5728 times, has been downloaded 1613 times. |
中文摘要 |
我們在一個簡單圖的邊上分別標上某相同集合裡非零的元素,如 果有一種標法能使得每個點的合是相同的值,我們就稱此圖為一個在 此集合上的半魔圖。並且稱在此標號下的這個相同的值為半魔圖指標, 簡稱指標。並把所有可能的指標所形成的集合稱為指標集。在這篇碩 士論文,我們決定了正規圖、完全二分圖、輪形圖和扇形圖在整數上 標號的指標集。另外,我們也決定了完全多分圖在整數上標號的指標 集會不會有零。 |
Abstract |
We call a finite simple graph G = (V (G),E(G)) to be Z-semimagic if it admits an edge labeling l : E(G) → Z {0} such that the induced vertex sum labeling l+(v) = uv∈E(G) l(uv) is constant. The constant is called a semimagic index, or an index for short, of G under the labeling l. We consider the set of all possible semimagic indices r such that G is Z-semimagic with a semimagic index r, and denote it by IZ(G). We call IZ(G) the index set of G with respect to Z. In this thesis, we decide the index set IZ(G) for G being regular graphs, complete bipartite graphs, wheel graphs and fan graphs. Also, we determine whether 0 ∈ IZ(G) for G being complete multi-partite graphs. |
目次 Table of Contents |
1 Introduction 1 2 Regular Graph 6 3 Complete Muti-partite Graph 11 4 Wheels and Fans 19 5 Conclusion 26 References 28 |
參考文獻 References |
[1] J. Sedl a cek , Problem 27, in "Thery of Graphs and Its Applications", Proc. Symp. Smolenice (1963), 163-167. [2] R. P. Stanley , Magic labeling of graphs, symmetric magic squares, systems of parameters and Cohen-Macaulay rings, Duke Math. J. 43 (1976), 511-531. [3] B. M. Stewart, Magic graphs, Canadian J. Math., 18 (1966), 1031-1059. [4] B. M. Stewart, Supermagic complete graphs, Canadian J. Math., 19 (1967) 427-438. [5] M. Doob, Characterizations of regular magic graphs, J. Combin. Theory, Ser. B, 25 (1978) 94-104. [6] R. H. Jeurissen, Magic graphs, a characterization, Europ. J. Combin., 9 (1988) 363-368. [7] U. Derings and H. Hunten, Magic graphs - A new characterization, Report No. 83265 - OR, Universitat Bonn April 1983, ISSN 0724-3138. [8] M. Doob, On the construction of magic graphs, Congr. Numer., 10 (1974) 361-374. [9] M. Trenkl er, Some results of magic graphs, graphs and other combinatorics topics, Teubner-Texte zur Mathematik - Band 59, Leipzig 1983, 328-332. [10] J. Mulbacher, Magische Quadrate und ihre Verallgemeinerung: ein graphentheoretisches Problem in: Graphs, Data Structures, Algorithms, Hensen Verlag, Munchen, 1979. [11] M. Doob, Generalizations of magic graphs, J. Combin. Theory, Ser. B 17 (1974) 205-217. [12] L. S andorov a and M.Trenkl er, On a generalization of magic graphs, Colloquia Math. Societatis J.Bolyai, 52 Combinatorics, North-Holland, Amsterdam 1988, 447-452. [13] T. M. Wang and C. Lin, Magic sum spectra of group magic graphs, India-Taiwan Conference on Discrete Mathematics,(2009), 9-12. [14] E. Salehi, Magic Graphs and Their Null Sets, Ars Combinatoria 82 (2007), 41-53 [15] E. Salehi, On Zero-Sum Magic Graphs and Their Null Sets, Bulletin of the Institute of Mathematical Sciences and Informations 3 (2008), 255-264. [16] T. M. Wang and C. Lin, On zero magic sums of integer magic graphs. [17] S. Jezn y and M. Trenkler, Characterization of magic graphs, Czechoslovak Mathemat- ical Journal 33 (1983), 435-438. |
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