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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/38640完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 張鎮華(Gerard-Jennhwa Chang) | |
| dc.contributor.author | Chin-Hung Lin | en |
| dc.contributor.author | 林晉宏 | zh_TW |
| dc.date.accessioned | 2021-06-13T16:40:12Z | - |
| dc.date.available | 2011-07-26 | |
| dc.date.copyright | 2011-07-26 | |
| dc.date.issued | 2011 | |
| dc.date.submitted | 2011-07-18 | |
| dc.identifier.citation | [1] AIM minimum rank-special graphs work group, Zero forcing sets and the minimum rank of graphs, Linear Algebra and its Applications 428 (2008) 1628--1648.
[2] F. Barioli ,W. Barrett, S. M. Fallat, H. T. Hall, L. Hogben, B. Shader, P. van den Driessche, and H. van der Holst, Zero forcing parameters and minimum rank problems, Linear Algebra and its Applications 433 (2010) 401--411. [3] F. Barioli, S. M. Fallat, H. T. Hall, D. Hershkowitz, L. Hogben, H. van der Holst, and B. Shader, On the minimum rank of not necessarily symmetric matrices: A preliminary study, Electronic Journal of Linear Algebra 18 (2009) 126--145. [4] F. Barioli, S. Fallat, and L. Hogben, Computation of minimal rank and path cover number for certain graphs, Linear Algebra and its Applications 392 (2004) 289--303. [5] F. Barioli, S. Fallat, and L. Hogben, On the difference between the maximum multiplicity and path cover number for tree-like graphs, Linear Algebra and its Applications 409 (2005) 13--31. [6] W. Barrett, H. van der Holst, and R. Loewy, Graphs whose minimal rank is two, Electronic Journal of Linear Algebra 11 (2004) 258--280. [7] L. DeLoss, J. Grout, T. McKay, J. Smith, and G. Tims, Program for calculating bounds on the minimum rank of a graph using Sage, http://arxiv.org/abs/0812.1616. [8] C. J. Edholm, L. Hogben, M. Huynh, J. LaGrange, and D. D. Row, Vertex and edge spread of zero forcing number, maximum nullity, and maximum rank of a graph, Hogben's Homepage. [9] S. Fallat and L. Hogben, The minimum rank of symmetric matrices described by a graph: A survey, Linear Algebra and its Applications 426 (2007) 558--582. [10] S. Fallat and L. Hogben, Variants on the minimum rank problem: A survey II, Hogben's Homepage. [11] R. Fernandes, On the maximum multiplicity of an eigenvalue in a matrix whose graph contains exactly one cycle, Linear Algebra and its Applications 422 (2007) 1--16. [12] H. van der Holst, The maximum corank of graphs with a 2-separation, Linear Algebra and its Applications 428 (2008) 1587--1600. [13] P. M. Nylen, Minimum-rank matrices with prescribed graph, Linear Algebra and its Applications 248 (1996) 303--316. [14] J. Sinkovic, Maximum nullity of outer planar graphs and the path cover number, Linear Algebra and its Applications 432 (2010) 2052--2060. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/38640 | - |
| dc.description.abstract | 一個圖G的最小秩問題是在討論所有可決定G的實對稱方陣中最小的秩，這等同於討論這群方陣中的最大零維數M(G)。零強迫數Z(G)是指最小零強迫集的個數，可用於最小秩問題的研究。而路徑覆蓋數P(G)是指可以用來覆蓋圖G點集的最小導出路徑數。當圖G中有截點時，我們提出一個公式用小圖的零強迫數來計算原圖G的零強迫數，並且討論在某些條件下P(G)會等於Z(G)，而這條件叫做強PZ條件。
零強迫數Z(G)是M(G)已知的上界。我們提出一個更緊的上界叫窮舉零強迫數~Z(G)，也就是Z(G)≥~Z(G)≥M(G)。並且提出一個篩選過程，使得在某些特殊例子中，可以得到比窮舉零強迫數再更緊的上界。 最後，我們找到一個反例，可以用來回答一個關於零強迫數在邊上的差值問題。 | zh_TW |
| dc.description.provenance | Made available in DSpace on 2021-06-13T16:40:12Z (GMT). No. of bitstreams: 1 ntu-100-R98221009-1.pdf: 1092152 bytes, checksum: 91697f86ef6237e38963b59a278ad8da (MD5) Previous issue date: 2011 | en |
| dc.description.tableofcontents | Acknowledgments i
Abstract (in Chinese) ii Abstract (in English) iii 1 Introduction 1 2 Vertex reduction for Z(G) and P(G) 3 3 Strong PZ condition 7 4 Graphs with large Z(G) −M(G) 9 5 Minimum rank of a pattern matrix 10 6 Rank of pattern matrix vs zero forcing number 13 7 Exhaustive zero forcing number of graphs 16 8 Sieving process 20 9 Summary about upper bounds of M(G) 32 10 A counterexample to a problem on edge spread 36 11 Further work 38 References 39 Appendix: List of computer programs 41 | |
| dc.language.iso | en | |
| dc.subject | 篩選過程 | zh_TW |
| dc.subject | 最小秩 | zh_TW |
| dc.subject | 零強迫數 | zh_TW |
| dc.subject | 窮舉零強迫數 | zh_TW |
| dc.subject | minimum rank | en |
| dc.subject | sieving process | en |
| dc.subject | exhaustive zero forcing number | en |
| dc.subject | zero forcing number | en |
| dc.title | 零強迫數在最小秩問題上的應用 | zh_TW |
| dc.title | Applications of zero forcing number to the minimum rank problem | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 99-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 葉鴻國(Hong-Gwa Yeh),顏經和(Jing-Ho Yan) | |
| dc.subject.keyword | 最小秩,零強迫數,窮舉零強迫數,篩選過程, | zh_TW |
| dc.subject.keyword | minimum rank,zero forcing number,exhaustive zero forcing number,sieving process, | en |
| dc.relation.page | 48 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2011-07-18 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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