Graphs and Matrices

2011. Copublication with the Hindustan Book Agency
ISBN: 978-1-84882-980-0
Verlag: Springer

Buch, Englisch, 171 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 290 g

Reihe: Universitext

Graphs and Matrices provides a welcome addition to the rapidly expanding selection of literature in this field. As the title suggests, the book’s primary focus is graph theory, with an emphasis on topics relating to linear algebra and matrix theory. Information is presented at a relatively elementary level with the view of leading the student into further research. In the first part of the book matrix preliminaries are discussed and the basic properties of graph-associated matrices highlighted. Further topics include those of graph theory such as regular graphs and algebraic connectivity, Laplacian eigenvalues of threshold graphs, positive definite completion problem and graph-based matrix games. Whilst this book will be invaluable to researchers in graph theory, it may also be of benefit to a wider, cross-disciplinary readership.

Zielgruppe

Graduate

Autoren/Hrsg.

Bapat, Ravindra B.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Operations Research Graphentheorie

Inhaltsverzeichnis

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.