ぱらぱらめくる『Graphs and Matrices』
Graphs and Matrices (Universitext)
- 作者: Ravindra B. Bapat
- 出版社/メーカー: Springer
- 発売日: 2014/10/02
- メディア: ペーパーバック
- この商品を含むブログを見る
- 目次
- 1 Preliminaries
- 2 Incidence Matrix
- 3 Adjacency Matrix
- 4 Laplacian Matrix
- 5 Cycles and Cuts
- 6 Regular Graphs
- 7 Algebraic Connectivity
- 8 Distance Matrix of a Tree
- 9 Resistance Distance
- 10 Laplacian Eigenvalues of Threshold Graphs
- 11 Positive Definite Completion Problem
- 12 Matrix Games Based on Graphs
- 本全体の大雑把なまとめはこちらに
- 細目次
- 1 Preliminaries
- 1.1 Matrices
- 1.2 Eigenvalues of symmetric matrices
- 1.3 Generalized inverses
- 1.4 Graphs
- 2 Incidence Matrix
- 2.1 Rank
- 2.2 Minors
- 2.3 Path matrix
- 2.4 Integer generalized inverses
- 2.5 Moore-Pnrose inverse
- 2.6 0-1 Incidence matrix
- 2.7 Matchings in bipartite graphs
- 3 Adjacency Matrix
- 3.1 Eigenvalues of some graphs
- 3.2 Determinant
- 3.3 Bountds
- 3.4 Energy of a graph
- 3.5 Antiadjacency matrix of a directed graph
- 3.6 Nonsingular trees
- 4 Laplacian Matrix
- 4.1 Basic properties
- 4.2 Computing Laplacian eigenvaues
- 4.3 Matrix-tree theorem
- 4.4 Bounds for Laplacian spectral radius
- 4.5 Edge-Laplacian of a tree
- 5 Cycles and Cuts
- 5.1 Fundamental cycles and fundamental cuts
- 5.2 Fundamental matrices
- 5.3 Minors
- 6 Regular Graphs
- 6.1 Perron-Frobenius theory
- 6.2 Adjacency algebra of a regular graph
- 6.3 Complement and line graph of a regular graph
- 6.4 Strongly regular graphs and friendship theorem
- 6.5 Grapshs with maximum energy
- 7 Algebraic Connectivity
- 7.1 Preliminary results
- 7.2 Classification of trees
- 7.3 Monotonicity properties of Fiedler vector
- 7.4 Bounds for algebraic connectivity
- 8 Distance Matrix of a Tree
- 8.1 Distance matrix of a graph
- 8.2 Distance matrix and Laplacian of a tree
- 8.3 Eigenvalues of the distance matrix of a tree
- 9 Resistance Distance
- 9.1 The triangle inequality
- 9.2 Network flows
- 9.3 A random walk on graphs
- 9.4 Effective resistance in electrical networks
- 9.5 Resistance matrix
- 10 Laplacian Eigenvalues of Thereshold Graphs
- 10.1 Majorization
- 10.2 Threshold graphs
- 10.3 Spectral integral variation
- 11 Positive Definite Completion Problem
- 11.1 Nonsingular completion
- 11.2 Chordal graphs
- 11.3 Positive definite completion
- 12 Matrix Games Based on Graphs
- 12.1 Matrix games
- 12.2 Vertex selection games
- 12.3 Tournament games
- 12.4 Incidence matrix games