Introduction to graph theory = 图论导引 /
副标题：无
作 者：Gary Chartrand, Ping Zhang著.
分类号：O157.5
ISBN：9787115148346
微信扫一扫,移动浏览光盘
简介
《图论导引(英文版)(本科)》介绍了图论的常用主题，同时也包含一些尚需进一步研究或未解决的议题，用于激发学生的创新能力。全书共分13章，前3章介绍一些基础知识，后面章节介绍了树、连通性、可遍历性、子图、匹配和因子分解、可平面性、图的着色、拉姆齐数、距离及控制等内容。《图论导引(英文版)(本科)》内容全面，证明与应用实例并举，还给出了证明技巧，书的最后提供了奇数题号的解答或提示。
《图论导引(英文版)(本科)》可作为本科生一学期课程教材，也可供图论爱好者自学使用。
目录
1. introduction .
1.1. graphs and graph models 1
1.2. connected graphs 9
1.3. common classes of graphs 19
1.4. multigraphs and digraphs 26
2. degrees
2.1. the degree of a vertex 31
2.2. regular graphs 38
2.3. degree sequences 43
2.4. excursion:graphs and matrices 48
2.5. exploration:irregular graphs 50
3. isomorphic graphs
3.1. the definiition of isomorphism 55
3.2. isomorphism as a relation 63
3.3. excursion:graphs and groups 66
3.4. excursion:reconstruction and solvability 76
4. trees
4.1. bridges 85
4.2. trees 87
4.3. the minimum spanning tree problem 94
.4.4. excursion:the number of spanning trees 101
5. connectivity
5.1. cut-vertices 107
5.2. blocks 111
5.3. connectivity 115
5.4. menger's theorem 124
5.5. exploration:geodetic sets 130
6. traversability
6.1. eulerian graphs 133
6.2. hamiltonian graphs 140
6.3. exploration:hamiltonian walks and numbers 152
6.4. excursion:the early books of graph theory 156
7. digraphs
7.1. strong digraphs 161
7.2. tournaments 169
7.3. excursion:decision-making 176
7.4. exploration:wine bottle problems 180
8. matchings and factorization
8.1. matchings 183
8.2. factorization .. 194
8.3. decompositions and graceful labelings 209
8.4. excursion:instant insanity 214
8.5. excursion:the petersen graph 219
8.6. exploration:γ-labelings of graphs 224
9. planarity
9.1. planar graphs 227
9.2. embedding graphs on surfaces 241
9.3. excursion:graph minors 249
9.4. exploration:embedding graphs in graphs 253
10. coloring
10.1. the four color problem 259
10.2. vertex coloring 267
10.3. edge coloring 280
10.4. excursion:the heawood map coloring theorem 288
10.5. exploration:local coloring 293
11. ramsey numbers
11.1. the ramsey number of graphs 297
11.2. turan's theorem 307
11.3. exploration:rainbow ramsey numbers 314
11.4. excursion:erdos numbers 321
12. distance
12.1. the center of a graph 327
12.2. distant vertices 333
12.3. excursion:locating numbers 341
12.4. excursion:detour and directed distance 346
12.5. exploration:channel assignment 351
12.6. exploration:distance between graphs 357
13. domination
13.1. the domination number of a graph 361
13.2. exploration:stratification 372
13.3. exploration:lights out 377
13.4. excursion:and still it grows more colorful 381
solutions and hints for odd-numbered exercises 383
references 411
index of names 423
index of mathematical terms 426
list of symbols ... 433
1.1. graphs and graph models 1
1.2. connected graphs 9
1.3. common classes of graphs 19
1.4. multigraphs and digraphs 26
2. degrees
2.1. the degree of a vertex 31
2.2. regular graphs 38
2.3. degree sequences 43
2.4. excursion:graphs and matrices 48
2.5. exploration:irregular graphs 50
3. isomorphic graphs
3.1. the definiition of isomorphism 55
3.2. isomorphism as a relation 63
3.3. excursion:graphs and groups 66
3.4. excursion:reconstruction and solvability 76
4. trees
4.1. bridges 85
4.2. trees 87
4.3. the minimum spanning tree problem 94
.4.4. excursion:the number of spanning trees 101
5. connectivity
5.1. cut-vertices 107
5.2. blocks 111
5.3. connectivity 115
5.4. menger's theorem 124
5.5. exploration:geodetic sets 130
6. traversability
6.1. eulerian graphs 133
6.2. hamiltonian graphs 140
6.3. exploration:hamiltonian walks and numbers 152
6.4. excursion:the early books of graph theory 156
7. digraphs
7.1. strong digraphs 161
7.2. tournaments 169
7.3. excursion:decision-making 176
7.4. exploration:wine bottle problems 180
8. matchings and factorization
8.1. matchings 183
8.2. factorization .. 194
8.3. decompositions and graceful labelings 209
8.4. excursion:instant insanity 214
8.5. excursion:the petersen graph 219
8.6. exploration:γ-labelings of graphs 224
9. planarity
9.1. planar graphs 227
9.2. embedding graphs on surfaces 241
9.3. excursion:graph minors 249
9.4. exploration:embedding graphs in graphs 253
10. coloring
10.1. the four color problem 259
10.2. vertex coloring 267
10.3. edge coloring 280
10.4. excursion:the heawood map coloring theorem 288
10.5. exploration:local coloring 293
11. ramsey numbers
11.1. the ramsey number of graphs 297
11.2. turan's theorem 307
11.3. exploration:rainbow ramsey numbers 314
11.4. excursion:erdos numbers 321
12. distance
12.1. the center of a graph 327
12.2. distant vertices 333
12.3. excursion:locating numbers 341
12.4. excursion:detour and directed distance 346
12.5. exploration:channel assignment 351
12.6. exploration:distance between graphs 357
13. domination
13.1. the domination number of a graph 361
13.2. exploration:stratification 372
13.3. exploration:lights out 377
13.4. excursion:and still it grows more colorful 381
solutions and hints for odd-numbered exercises 383
references 411
index of names 423
index of mathematical terms 426
list of symbols ... 433
Introduction to graph theory = 图论导引 /
- 名称
- 类型
- 大小
光盘服务联系方式: 020-38250260 客服QQ：4006604884
云图客服：
用户发送的提问，这种方式就需要有位在线客服来回答用户的问题，这种 就属于对话式的,问题是这种提问是否需要用户登录才能提问
Video Player
×
Audio Player
×
pdf Player
×
