雙環網路距離二以內的控制問題

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張凱媛(Kai-Yuan Zhen) 查詢紙本館藏

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數學系

論文名稱

雙環網路距離二以內的控制問題
(Distance-two domination of double-loopnetworks.)

相關論文

★ Signed Domination in Block Graphs	★ Wide diameters and Rabin numbers of generalized folded hypercube networks
★ Distance-two domination of graphs	★ Strong Rabin Numbers on Cartesian Products of Graphs
★ Global defensive alliances in double-loop networks	★ 廣義彼得森圖形的控制數

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摘要(中)

由於實際資源分享問題，在此篇論文中我們考慮到控制問題的變形，稱為距離二以內的控制問題。
這篇論文架構如下：第一節、介紹基本的定義，第二節、決定DL(n;1,2)控制數。第三節、決定DL(n;1,3)控制數。第四節、決定DL(n;1,n/2)控制數。最後一節是針對一般圖形，控制數的研究。

摘要(英)

Due to a practically resource sharing problem, we consider a variation of the domination problem in this thesis which we call the distance-two domination problem.
This thesis is organized as follows. Section 1 gives basic definitions and notation. Section 2 investigates the distance-two domination of (n;1,2). Section 3 investigates the distance-two domination of (n;1,3). Section 4 investigates the distance-two domination of (n;1,n/2). We provide the integer programming method to canvass r_3,2,1(G) in the final section.

關鍵字(中)

關鍵字(英)

★ 1-domination number
★ Distance-two domination
★ double-loop networks
★ D_3
★ 2
★ 1-dominating set

論文目次

Abstract (in English)................................ ii
Contents............................................. iii
1 Introduction ...................................... 1
2 Distance-two domination of DL(n;1,2)............... 9
3 Distance-two domination of DL(n;1,3)............... 11
4 Distance-two domination of DL(n;1,n/2)............. 17
5 Further research with integer programming.......... 20
References........................................... 23

參考文獻

References
[1] B. Alspach and T. D. Parsons, Isomorphism of circulant graphs and digraphs,
Discrete Mathematics 25 (1979), 97-108.
[2] F. Boesch and R. Tindell, Circulants and Their Connectivities, Journal of
Graph Theory 8 (1984), 487-499.
[3] T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Domination in Graphs:
Advanced Topices, Marcel Dekker, NY (1998).
[4] T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Fundamentals of Domination
in Graphs, Marcel Dekker, NY (1998).
[5] T. W. Haynes and P. J. Slater, Paired-domination in graphs, Networks 32
(1998), 199-206.
[6] F. R. Hsu, Distance-two domination of graphs, Master Thesis, National Central
University (2006).
[7] S. H. Huang, F. K. Hwang, and Y. H. Liu, Equivalent Double-Loop Networks,
Taiwanese Journal of Mathematics 4 (2000), 661-668.
[8] F. K. Hwang, A complementary survey on Double-Loop Network, Theoretical
Computer Science 263 (2001), 211-229.
[9] F. K. Hwang, P. E. Wright, and X. D. Hu, Exact Reliabilities of Most Reliable
Double-Loop Networks, Networks 30 (1997), 81-90.
[10] J. S. Lee, J. K. Lan, and C. Y. Chen, On Degenerate Double-Loop L-shapes,
Journal of Interconnection Networks 7 (2006), 195-215.
[11] D. B. West, Introduction to Graph Theory, 2nd ed., Prentice-Hall, NJ (2001).

指導教授

廖勝強(Sheng-Chyang Liaw)

審核日期

2009-6-26

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