# ぱらぱらめくる『Graphs and Matrices』

Graphs and Matrices (Universitext)

• 目次
• 1 Preliminaries
• 2 Incidence 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
• 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
• 3.1 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