The theory of graphs 图论

From the circuit diagrams of physics and electronics to psychology's sociograms and the communications networks employed by opera-tional research, an extraordinary variety of disciplines rely on graphs to convey fundamentals as well as finer points. With this concise and well-written text, any reader possessing a firm grasp of general math-ematics can follow the development of graph theory and learn to apply its principles in methods both formal and abstract.
The first full-length book in English on graph theory, this volume is the work of a distinguished mathematician who has made significant original contributions to the subject. His frequent use of practical examples illustrates the theory's broad range of applications, provid-ing a versatile mathematical technique appropriate to the behavioral sciences, information theory, cybernetics, and other areas, in addi-tion to mathematical disciplines such as set and matrix theory.
The author begins with the simplest theorems, stated in the most general terms possible for economy of thought and exposition. He gradually builds to more complex theorems, expressed in more exact-ing proofs and reflecting the results of extensive studies. Definitions from algebra and the theory of sets appear at the start and are sup-plemented as needed. Students, teachers, and anyone interested in effective communication of research results will find this text a valuable source of instruction.

Introduction
1 General Definitions
2 Descendance Relations
3 The Ordinal Function and the Grundy Function on an Infinite Graph
4 The Fundamental Numbers of the Theory of Graphs
5 Kernels of a Graph
6 Games on a Graph
7 The Problem of the Shortest Route
8 Transport Networks
9 The Theorem of the Demi-Degress
10 Matching of a Simple Graph
11 Factors
12 Centres of a Graph
13 The Diameter of a Strongly Connected Graph
14 The Matrix Associated with a Graph
15 Incidence Matrices
16 Trees and Arborescences
17 Euler's Problem
18 Matching in the General Case
19 Semi-Factors
20 The Connectivity of a Graph
21 Planar Graphs
Appendix 1 Note on the General Thoery of Games
Appendix 2 Note on Transport Problems
Bibliography
List of Symbols
Index of Terms Used