《圖論基礎》除了介紹圖論的基本概念和簡單結構理論外，主要研究總結了近些年來比較熱門的關於圖的鄰接譜、圖的匹配多項式、圖的著色、圖的色多項式、圖的拉普拉斯多項式和圖的準拉普拉斯多項式的一些主要成果。出版社是清華大學出版社。
基本介紹
圖書信息,內容簡介,圖書目錄,
圖書信息
書 名: 圖論基礎
ISBN: 9787302241638
出版時間： 2011年8月1日
內容簡介
為了方便讀者進行研究和參考，我們也采編了一些和圖論問題相關的線性代數、矩陣論的理論知識。在書的後面給出了基本符號及中英文對照表，以方便讀者查閱參考。
《圖論基礎》內容詳細，證明簡潔，並且在每章後面提供了一些新的研究內容與素材並配以一定量的習題，可作為數學與套用數學專業高年級的專業選修課和圖論方向的一年級的碩士研究生課程的教材，也可作為廣大圖論研究工作者的參考用書。
圖書目錄
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
