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課程名稱 |
代數圖論
ALGEBRAIC GRAPH THEORY |
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開課學期 |
97-1 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
張鎮華 |
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課號 |
MATH8701 |
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課程識別碼 |
221 U4020 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期二3,4(10:20~12:10)星期四1(8:10~9:00) |
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上課地點 |
舊數103舊數103 |
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備註 |
總人數上限：30人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/971Algebraic_Graph_T |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
1. Genearlized polygons and Moore graphs
2. Kneser graphs
3. Matrix Theory
4. Interlacing
5. Strongly regular graphs
6. The Laplacian of a graph |
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課程目標 |
Algebraic graph theory is concerned with the use of algebraic techniques in the study of graphs. The aim is to translate properties of graphs into algebraic properties and then, using the results and methods of algebra, to reduce theorems on graphs. The purpose of this course is to introduce basic notation and tools of algebraic graph theory. |
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課程要求 |
Basic knowledge on linear algebra, such as rank and eigenvalue. |
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預期每週課後學習時數 |
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Office Hours |
另約時間 備註： Make appointmtnt if necessary. |
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指定閱讀 |
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參考書目 |
0. Lecture note "Spectra of graphs" by Andries E. Brouwer and Willem H.
Haemers. (Textbook)
1. C. Godsil and G. Royle, Algebraic Graph Theory, Springer, 2001.
2. N. Biggs, Algebraic Graph Theory, Second Edition, Cambridge University
Press, 1993.
3. R. A. Brualdi, Combinatorial Matrix Classes, Cambridge University Press,
2006.
4. R. A. Brualdi and H. J. Ryser, Combinatorial Matrix Theory, Cambridge
Univsersity Press, 1991.
5. P. J. Cameron, Combinatorics: Topics, Techniques, Algorithms, Cambridge
University Press, 1994.
6. C. D. Godsil, Algebraic Combinatorics, Chapman & Hall, 1993.
7. W. T. Tutte, Graph Theory, Addison-Wesley, 1984. |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
期中考 |
35% |
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2. |
期末考 |
35% |
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3. |
平時成績及作業 |
30% |
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週次 |
日期 |
單元主題 |
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第1週 |
9/16,9/18 |
0. Introduction |
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第2週 |
9/23,9/25 |
1. Graph spectrum |
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第3週 |
9/30,10/02 |
1. Graph spectrum |
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第4週 |
10/07,10/09 |
2. Linear algebra |
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第5週 |
10/14,10/16 |
2. Linear algebra |
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第6週 |
10/21,10/23 |
3. Graph spectrum (II) |
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第7週 |
10/28,10/30 |
3. Graph spectrum (II) |
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第8週 |
11/04,11/06 |
4. Substructures |
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第9週 |
11/11,11/13 |
4. Substructures
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第10週 |
11/18,11/20 |
8. Strongly regular graphs
(Midterm on 11/18) |
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第11週 |
11/25,11/27 |
8. Strongly regular graphs |
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第12週 |
12/02,12/04 |
8. Strongly regular graphs |
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第13週 |
12/09,12/11 |
11. Distance regular graphs |
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第14週 |
12/16,12/18 |
Rank of a graph |
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第15週 |
12/23,12/25 |
Minimum rank of a graph |
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第16週 |
12/30,1/01 |
Minimum rank of a graph |
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第17週 |
1/06,1/08 |
Minimum rank of a graph |
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第18週 |
1/13,1/15 |
Final Examination at 18:30 of 14 January |
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