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Student Number 952201004 Author Kai-Yuan Zhen(±i³Í´D) Author's Email Address No Public. Statistics This thesis had been viewed 875 times. Download 356 times. Department Mathematics Year 2008 Semester 2 Degree Master Type of Document Master's Thesis Language English Title Distance-two domination of double-loop

networks.Date of Defense 2008-06-19 Page Count 23 Keyword 1-dominating set 1-domination number 2 D_3 Distance-two domination double-loop networks Abstract 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.Table of Content 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........................................... 23Reference References

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[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).

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(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).Advisor Sheng-Chyang Liaw(¹ù³Ó±j)

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952201004.pdf Date of Submission 2009-06-26

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