# Graphs and Matrices

• Ravindra B. Bapat
Textbook

Part of the Universitext book series (UTX)

1. Front Matter
Pages i-xi
2. Ravindra B. Bapat
Pages 1-11
3. Ravindra B. Bapat
Pages 13-26
4. Ravindra B. Bapat
Pages 27-48
5. Ravindra B. Bapat
Pages 49-59
6. Ravindra B. Bapat
Pages 61-68
7. Ravindra B. Bapat
Pages 69-85
8. Ravindra B. Bapat
Pages 87-99
9. Ravindra B. Bapat
Pages 101-114
10. Ravindra B. Bapat
Pages 115-130
11. Ravindra B. Bapat
Pages 131-144
12. Ravindra B. Bapat
Pages 145-155
13. Ravindra B. Bapat
Pages 157-164
14. Ravindra B. Bapat
Pages 165-177
15. Back Matter
Pages 179-193

### Introduction

This new edition 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.

Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book.

In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reorganized.

Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory, it will also benefit readers in the sciences and engineering.

### Keywords

Algebraic Connectivity Graph Theory Linear and Multilinear Algebras Matrix Techniques Matrix Theory

#### Authors and affiliations

• Ravindra B. Bapat
• 1
1. 1.Indian Statistical InstituteNew DelhiIndia

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4471-6569-9
• Copyright Information Springer-Verlag London 2014
• Publisher Name Springer, London
• eBook Packages Mathematics and Statistics
• Print ISBN 978-1-4471-6568-2
• Online ISBN 978-1-4471-6569-9
• Series Print ISSN 0172-5939
• Series Online ISSN 2191-6675
• Buy this book on publisher's site