國立中山大學,National Sun Yat-sen University,學位論文,thesis/dissertation,路徑r-局部控制碼之研究,The study of r-locating dominating codes in paths

論文名稱 Title	路徑r-局部控制碼之研究 The study of r-locating dominating codes in paths
系所名稱 Department	應用數學系 Department of Applied Mathematics
畢業學年期 Year, semester	102 學年度第 2 學期 The spring semester of Academic Year 102	語文別 Language	英文 English
學位類別 Degree	碩士 Master	頁數 Number of pages	21
研究生 Author	林筱芸 Hsiao- Yun Lin
指導教授 Advisor	董立大 Li-Da Dong
召集委員 Convenor	官大智 D.J. guan
口試委員 Advisory Committee	林承穎, 王彩蓮 Cheng-Ying Lin; Tsai-Lien Wong
口試日期 Date of Exam	2014-07-15	繳交日期 Date of Submission	2014-07-16
關鍵字 Keywords	局部控制碼、控制碼、圖 locating-dominating code, graph, dominating
統計 Statistics	本論文已被瀏覽 5772 次，被下載 226 次 The thesis/dissertation has been browsed 5772 times, has been downloaded 226 times.

中文摘要
圖的r-局部控制碼是由 Colbourn、Slater、和 Stewart 提出。Slater 證明了 M^LD_1(Pn) =⌈2n/5⌉。Honkaia 證明了 M^LD_2(Pn) = ⌈(n+1)/3⌉。Exoo、Junnila和Laihonen獲得了M^LD_r(Pn)的值，當(3 ≤ r ≤ 4)和(r ≥ 5且2 ≤ n ≤ 7r + 3)。本篇論文，我們判斷了M^LD_r(Pn)的值，當r ≥ 5且7r + 4 ≤ n ≤ 11r + 5.
Abstract
The locating-dominating code of graph was introduced by Colbourn, Slater, and Stewart . Slatert proved that M^LD_1(Pn) = =⌈2n/5⌉. Honkaia proved that M^LD_2(Pn) = ⌈(n+1)/3⌉. Exoo, Junnila, and Laihonen determined M^LD_r(Pn) for (3 ≤ r ≤ 4) and (r ≥ 5 and 2 ≤ n ≤ 7r + 3). In this thesis, we determine M^LD_r(Pn) for r ≥ 5 and 7r + 4 ≤ n ≤ 11r + 5.

目次 Table of Contents
論文審定書 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i 中文摘要 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Previous results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

參考文獻 References
[1] N. Bertrand, I. Charon, O. Hudry, and A. Lobstein, Identifying and locating- dominating codes on chains and cycles, European J. Combin. 25 (7) (2004) 969-987. [2] I. Charon, O. Hucdry, and A. Lobstein, Minimizing the size of aan identifing or locating-dominating code in a graph is NP-hard, Theoret. comput. Sci. 290 (2003), no. 3, 2109-2120. [3] C. J. Colbourn, P. J. Slater, and L. K. Stewart, Locating-dominating sets in series parallel network, Congressus Numerantium, vol.56 (1987) 135-162. [4] G. Exoo, V. Junnila, and T. Laihonen, Locating-dominating codes in paths, Discrete Mathematics 311 (2011) 1863-1873. [5] I. Honkala, On r-locating-dominating set in paths, European J. Combin. 30(4)(2009)1022-1025. [6] P. J. Slater, Pomination and locating in acyclic graphs, Networks 17(1) (1987)55-64. [7] M. G. Karpovsky, K. Chakrarry, L.B. Levitin, On a new class of codes for identifying vertices in graphs, IEEE Transactions on Information Theory 44 (1998)599-611.

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