A First Course in Graph Theory-图论基础教程 目录

contents
preface iii
chapter 1 basic concepts of graphs 1
1.1 graph and graphical representation.2
1.2 graph isomorphism.10
1.3 vertex degrees 20
1.4 subgraphs and operations 32
1.5 walks， paths and connection 44
chapter 2 advanced concepts of graphs 53
2.1 distances and diameters53
2.2 circuits and cycles 66
2.3 eulerian graphs 79
2.4 hamiltonian graphs 88
2.5 matrix representations of graphs 103
2.6 exponents of primitive matrices 115
chapter 3 trees and graphic spaces 125
3.1 trees and spanning trees.125
3.2 vector spaces of graphs 143
3.3 enumeration of spanning trees 157
3.4 the minimum connector problem. 166
3.5 the shortest path problem.173
3.6 the electrical network equations 182
chapter 4 plane graphs and planar graphs 187
4.1 plane graphs and euler’s formula187
4.2 kuratowski’s theorem.200
4.3 dual graphs.209
4.4 regular polyhedra.214
4.5 layout of printed circuits 217
chapter 5 flows and connectivity.225
5.1 network flows 225
5.2 menger’s theorem.230
5.3 connectivity.244
5.4 design of transport schemes 260
5.5 design of optimal transport schemes 268
5.6 the chinese postman problem 273
5.7 construction of squared rectangles.280
chapter 6 matchings and independent sets 287
6.1 matchings 287
6.2 independent sets 302
6.3 the personnel assignment problem.310
6.4 the optimal assignment problem. 319
6.5 the travelling salesman problem.327
chapter 7 colorings and integer flows 336
7.1 vertex-colorings.336
7.2 edge-colorings 348
7.3 face-coloring and four-color problem.356
7.4 integer flows and cycle covers368
chapter 8 graphs and groups 383
8.1 group representation of graphs383
8.2 transitive graphs 389
8.3 graphic representation of groups 400
8.4 design of interconnection networks 409
bibliography 421
list of notations 440
index 444

自然科学 数学 代数数论组合理论

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