Graphs and matrices

By: R.B. BapatMaterial type: TextTextSeries: Texts and Readings in Mathematics ; Vol. 58Publication details: New Delhi: Hindustan Book Agency, [c2018]Edition: 2nd edDescription: 187 pISBN: 9789380250694LOC classification: QA166.BAP
Contents:
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
Summary: 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.
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Item type Current library Collection Shelving location Call number Status Notes Date due Barcode Item holds
Book Book ICTS
Mathematics Rack No 2 QA166.BAP (Browse shelf (Opens below)) Available Billno: 45814 ; Billdate: 11.03.2020 02401
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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.

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