Universitext

Graphs and Matrices

Authors: Bapat, Ravindra B.

  • Presents a useful overview of selected topics in algebraic graph theory
  • Extensive coverage of topics provides a welcome prompt for further exploration
  • A broad range of material that may be applied to a selection of sub-disciplines within science and engineering
  • The inclusion of exercises enables practical learning throughout the book
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eBook $44.99
price for USA (gross)
  • ISBN 978-1-84882-981-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-1-84882-980-0
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
About this Textbook

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 greater than other standard references on algebraic graph theory, and the important matrices associated with graphs such as 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, and the inclusion of exercises enables practical learning throughout the book. It may also be applied to a selection of sub-disciplines within science and engineering.

Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory who want to be acquainted with matrix theoretic ideas used in graph theory, it will also benefit a wider, cross-disciplinary readership.

Reviews

From the reviews:

“Students who have completed introductory courses in linear algebra and graph theory should be able to understand and benefit from this book. It is divided into 12 chapters. … Each chapter includes … a good number of references in a bibliographic format. … A complete bibliography with all of the chapter references is available at the end of the book. Summing Up: Recommended. Upper-division undergraduates through researchers/faculty.” (J. T. Saccoman, Choice, Vol. 49 (1), September, 2011)

“The book is a study of matrices associated to graphs based on linear algebra techniques. … The exposition is exact and clear. The proofs are presented in detail and should be understood with no difficulty by any reader with a preliminary background in linear algebra. … Hence, the book can be used as a textbook for undergraduate level courses. Graduate students and researchers working on spectral graph theory or closely related fields will also benefit from the book.” (Behruz Tayfeh-Rezaie, Mathematical Reviews, Issue 2012 f)

“A student having completed introductory courses in Linear Algebra and Graph Theory should be able to understand and benefit from this text. At the end of each of the twelve chapters there are a few exercises and a good number of references. … this text would be a fine resource for an advanced undergraduate or someone wishing to learn more about this synergistic field of study.” (John T. Saccoman, The Mathematical Association of America, June, 2011)


Table of contents (12 chapters)

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-1-84882-981-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-1-84882-980-0
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
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Bibliographic Information

Bibliographic Information
Book Title
Graphs and Matrices
Authors
Series Title
Universitext
Copyright
2010
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
Distribution Rights
Distribution rights in India: Hindustan Book Agency (HBA), New Delhi, India
eBook ISBN
978-1-84882-981-7
DOI
10.1007/978-1-84882-981-7
Softcover ISBN
978-1-84882-980-0
Series ISSN
0172-5939
Edition Number
1
Number of Pages
IX, 171
Additional Information
Jointly published with Hindustan Book Agency (HBA), New Delhi, India
Topics