《图论基础》是在作者张海良、苏岐芳、林荣斐几年来开设“图论”双语教学所使用的自编讲义的基础上整理而成的。详细介绍了图的基本概念、图的谱、树、连通性、欧拉与哈密尔顿图以及图的匹配多项式、图的着色、色多项式和图的准拉普拉斯谱等近几年的一些主要成果，同时也采编了一些解决图论问题的有关线性代数，矩阵论的理论知识。并且，在每章后面提供了一定量的习题，此外，作为对图论知识的应用在每章给出一个GROUP PROJECT供读者练习。总体上来讲，本教材内容丰富并且由浅入深，是一本图论入门书，也是对图的匹配多项式理论感兴趣的读者的一本较全面的参考书。

张海良、苏岐芳、林荣斐编著的《图论基础》除了介绍图论的基本概念和简单结构理论外，主要研究总结了近些年来比较热门的关于图的邻接谱、图的匹配多项式、图的着色、图的色多项式、图的拉普拉斯多项式和图的准拉普拉斯多项式的一些主要成果。为了方便读者进行研究和参考，我们也采编了一些和图论问题相关的线性代数、矩阵论的理论知识。在书的后面给出了基本符号及中英文对照表，以方便读者查阅参考。

《图论基础》内容详细，证明简洁，并且在每章后面提供了一些新的研究内容与素材并配以一定量的习题，可作为数学与应用数学专业高年级的专业选修课和图论方向的一年级的硕士研究生课程的教材，也可作为广大图论研究工作者的参考用书。

Preface in Chinese

Chapter 1 Basic concepts

 1.1 Graph and simple graph

 1.2 Graph operations

 1.3 Isomorphism

 1.4 Incident and adjacent matrix

 1.5 The spectrum of graph

 1.6 The spectrum of several graphs

 1.7 Results from matrix theory

 1.8 About the largest zero of characteristic polynomials

 1.9 Spectrum radius

Chapter 2 path and cycle

 2.1 The path

 2.2 The cycle

 2.3 The diameter of a graph and its complement graph

Chapter 3 Tree

 3.1 Tree

 3.2 Spanning tree

 3.3 A bound for the tree number of regular graphs

 3.4 Cycle space and bound space of a graph

Chapter 4 Connectivity

 4.1 Cut edges

 4.2 Cut vertex

 4.3 Block

 4.4 Connectivity

Chapter 5 Euler and Hamilton graphs

 5.1 Euler path and circuits

 5.2 Hamilton graph

Chapter 6 Matching and matching polynomial

 6.1 Matching

 6.2 Bipartite graph and perfect matching

 6.3 Matching polynomial

 6.4 The relation between spectrum and matching polynomial

 6.5 Relation between several graphs

 6.6 Several matching equivalent and matching unique graphs

 6.7 The Hosoya index of several graphs

 6.8 Two trees with minimal Hosoya index

 6.9 Recent results in matching

Chapter 7 Laplacian and Quasi-Laplacian spectrum

 7.1 Sigma function

 7.2 The spanning tree and sigma function

 7.3 Quasi-Laplacian Spectrum

 7.4 Basic lemmas

 7.5 Main results

 7.6 Three different spectrum of regular graphs

Chapter 8 More theorems form matrix theory

 8.1 The irreducible matrix

 8.2 Cauchy's interlacing theorem

 8.3 The eigenvalues of A（G） and graph structure

Chapter 9 Chromatic polynomial

 9.1 Induction

 9.2 Two different formula for chromatic polynomial

 9.3 Chromatic polynomials for several type of graphs

 9.4 Estimate the color number

References

Bibliography