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
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