Graphs and Matrices

• Main Author: Bapat, R. B. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: London : Springer London, 2010.
• Series: Universitext
• Subjects: Mathematics.; Matrix theory.; Linear and Multilinear Algebras, Matrix Theory.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-1-84882-981-7

Whilst it is a moot point amongst researchers, linear algebra is an important component in the study of graphs. This book illustrates the elegance and power of matrix techniques in the study of graphs by means of several results, both classical and recent. The emphasis on matrix techniques is greate...

Table of Contents:

• Preliminaries
• Incidence Matrix
• Adjacency Matrix
• Laplacian Matrix
• Cycles and Cuts
• Regular Graphs
• Algebraic Connectivity
• Distance Matrix of a Tree
• Resistance Distance
• Laplacian Eigenvalues of Threshold Graphs
• Positive Definite Completion Problem
• Matrix Games Based on Graphs
• Hints and Solutions to Selected Exercises.