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博碩士論文 etd-0822111-161243 詳細資訊
Title page for etd-0822111-161243
論文名稱
Title
在整數上標號的半魔圖
The Z-Semimagic of Some Graphs
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
35
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
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
統計
Statistics
本論文已被瀏覽 5728 次,被下載 1613
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
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Smolenice (1963), 163-167.
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[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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