論文使用權限 Thesis access permission:校內校外完全公開 unrestricted
開放時間 Available:
校內 Campus: 已公開 available
校外 Off-campus: 已公開 available
論文名稱 Title |
圖形的凸集譜及強凸集譜 The Convexity Spectra and the Strong Convexity Spectra of 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 |
26 |
|
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 |
2005-05-27 |
繳交日期 Date of Submission |
2005-07-28 |
關鍵字 Keywords |
圖形凸集譜、完全圖、凸集、凸集數 Convex set, convexity number, convexity spectrum, complete graph |
||
統計 Statistics |
本論文已被瀏覽 5771 次,被下載 1927 次 The thesis/dissertation has been browsed 5771 times, has been downloaded 1927 times. |
中文摘要 |
對一連通有向圖D中,令S為頂點集V(D)的一子集。若對S內任意兩頂點x,y,每條最短x-y有向路徑及最短y-x有向路徑上的頂點皆落在S內,則稱S為D的一個凸子集。且D的最大凸子集且為真子集的集合大小即為D的凸集數,記為con(D)。 令S_{C}(K_{n})={con(D)|D為一n頂點競賽圖}且S_{SC}(K_{n})={con(D)|D為一n頂點強連通競賽圖},我們得到S_{C}(K_{3})={1,2}及當n大於等於4時,S_{C}(K_{n})={1,3,4,...,n-1}。我們也得到S_{SC}(K_{3})={1}及當n大於等於4時,S_{SC}(K_{n})={1,3,4,...,n-2}。 我們也找到對任意的整數n、m、k,當n大於等於5、k介於3到n-2之間且m介於n+1到n(n-1)/2之間時,存在一強連通有向圖D的頂點數為n、邊數為m,且凸集數為k。 |
Abstract |
Given a connected oriented graph D, we say that a subset S of V(D) is convex in D if, for every pair of vertices x, y in S, the vertex set of every x-y geodesic (x-y shortest dipath) and y-x geodesic in D is contained in S. The convexity number con (D) of a nontrivial connected oriented graph D is the maximum cardinality of a proper convex set of D. Let S_{C}(K_{n})={con(D)|D is an orientation of K_{n}} and S_{SC}(K_{n})={con(D)|D is a strong orientation of K_{n}}. We show that S_{C}(K_{3})={1,2} and S_{C}(K_{n})={1,3,4,...,n-1} if n >= 4. We also have that S_{SC}(K_{3})={1} and S_{SC}(K_{n})={1,3,4,...,n-2} if n >= 4 . We also show that every triple n, m, k of integers with n >= 5, 3 <= k <= n-2, and n+1 <= m <= n(n-1)/2, there exists a strong connected oriented graph D of order n with |E(D)|=m and con (D)=k. |
目次 Table of Contents |
1 Introduction 2 Previous results 3 The main results 3-1 Strong convexity spectra of complete graphs 3-2 Constructing oriented graphs with fixed order, size, and convexity number 4 References |
參考文獻 References |
[1] G. Chartrand, C.E. Wall, P. Zhang, The convexity number of a graph, Graphs Combin. 18 (2002), no. 2, 209-217. [2] G. Chartrand, J.F. Fink, P. Zhang, Convexity in oriented graphs, Discrete Appl. Math. 116 (2002), no. 1-2, 115-126 [3] S.R. Canoy, I.J.L. Garces, Convex sets under some graph operations, Graphs Combin. 18 (2002), no. 4, 787-793. [4] G. Chartrand, P. Zhang, Convex sets in graphs, Congr. Numer. 136 (1999), 19-32. [5] D.C. Isaksen, B. Robinson, Triangle-free polyconvex graphs}, Ars Combin. 64 (2002), 259-263. [6] G. Chartrand, P. Zhang, The forcing convexity number of a graph, Czechoslovak Math. J. 51(126) (2001), no. 4, 847-858. [7] F. Harary, J. Nieminen, Convexity in graphs, J. Differ. Geom. 16 (1981), 185-190. [8] G. Chartrand, L. Lesniak, Graphs and Digraphs, Chapman and Hall, 1996. [9] D.B. West, Introduction to Graph Theory, Prentice Hall, 2001. [10] F. Buckley, F. Harary, Distances in Graphs, Addison-Wesley, Redwood City, CA, 1990. |
電子全文 Fulltext |
本電子全文僅授權使用者為學術研究之目的,進行個人非營利性質之檢索、閱讀、列印。請遵守中華民國著作權法之相關規定,切勿任意重製、散佈、改作、轉貼、播送,以免觸法。 論文使用權限 Thesis access permission:校內校外完全公開 unrestricted 開放時間 Available: 校內 Campus: 已公開 available 校外 Off-campus: 已公開 available |
紙本論文 Printed copies |
紙本論文的公開資訊在102學年度以後相對較為完整。如果需要查詢101學年度以前的紙本論文公開資訊,請聯繫圖資處紙本論文服務櫃台。如有不便之處敬請見諒。 開放時間 available 已公開 available |
QR Code |