A First Course in Graph Theory

Preface
Chapter 1 Basic Concepts of Graphs
　1.1　Graph and Graphical Representation
　1.2　Graph Isomorphism
　1.3　Vertex Degrees
　1.4　Subgraphs and Operations
　1.5　Walks， Paths and Connection
Chapter 2 Advanced Concepts of Graphs
　2.1　Distances and Diameters
　2.2　Circuits and Cycles
　2.3　Eulerian Graphs
　2.4　Hamiltonian Graphs
　2.5　Matrix Representations of Graphs
　2.6　Exponents of Primitive Matrices
Chapter 3 Trees and Graphic Spaces
　3.1　Trees and Spanning Trees
　3.2　Vector Spaces of Graphs
　3.3　Enumeration of Spanning Trees
　3.4　The Minimum Connector Problem
　3.5　The Shortest Path Problem
　3.6　The Electrical Network Equations
Chapter 4 Plane Graphs and Planar Graphs
　4.1　Plane Graphs and Euler’s Formula
　4.2　Kuratowski’s Theorem
　4.3　Dual Graphs
　4.4　Regular Polyhedra
　4.5　Layout of Printed Circuits
Chapter 5 Flows and Connectivity
　5.1　Network Flows
　5.2　Menger’s Theorem
　5.3　Connectivity
　5.4　Design of Transport Schemes
　5.5　Design of Optimal Transport Schemes
　5.6　The Chinese Postman Problem
　5.7　Construction of Squared Rectangles
Chapter 6 Matchings and Independent Sets
　6.1　Matchings
　6.2　Independent Sets
　6.3　The Personnel Assignment Problem
　6.4　The Optimal Assignment Problem
　6.5　The Travelling Salesman Problem
Chapter 7 Colorings and Integer Flows
　7.1　Vertex-Colorings
　7.2　Edge-Colorings
　7.3　Face-Coloring and Four-Color Problem
　7.4　Integer Flows and Cycle Covers
Chapter 8 Graphs and Groups
　8.1　Group Representation of Graphs
　8.2　Transitive Graphs
　8.3　Graphic Representation of Groups
　8.4　Design of Interconnection Networks
Bibliography
List of Notations
Index