R.B. Bapat
Graphs and matrices - 2nd ed. - New Delhi: Hindustan Book Agency, [c2018] - 187 p - Texts and Readings in Mathematics Vol. 58 .
1 Preliminaries
2 Incidence Matrix
3 Adjacency Matrix
4 Laplacian Matrix
5 Cycles and Cuts
6 Regular Graphs
7 Line Graph of a Tree
8 Algebraic Connectivity
9 Distance Matrix of a Tree
10 Resistance Distance
11 Laplacian Eigenvalues of Threshold Graphs
12 Positive Definite Completion Problem
13 Matrix Games Based on Graphs
This book illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph.
9789380250694
QA166.BAP
Graphs and matrices - 2nd ed. - New Delhi: Hindustan Book Agency, [c2018] - 187 p - Texts and Readings in Mathematics Vol. 58 .
1 Preliminaries
2 Incidence Matrix
3 Adjacency Matrix
4 Laplacian Matrix
5 Cycles and Cuts
6 Regular Graphs
7 Line Graph of a Tree
8 Algebraic Connectivity
9 Distance Matrix of a Tree
10 Resistance Distance
11 Laplacian Eigenvalues of Threshold Graphs
12 Positive Definite Completion Problem
13 Matrix Games Based on Graphs
This book illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph.
9789380250694
QA166.BAP