Distance Regular Graphs

Author : Andries E. Brouwer
Publisher : Springer Science & Business Media
ISBN 13 : 3642743412
Total Pages : 513 pages
Book Rating : 4.12/5 ( download)

DOWNLOAD NOW!

Download or read book Distance-Regular Graphs written by Andries E. Brouwer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ever since the discovery of the five platonic solids in ancient times, the study of symmetry and regularity has been one of the most fascinating aspects of mathematics. Quite often the arithmetical regularity properties of an object imply its uniqueness and the existence of many symmetries. This interplay between regularity and symmetry properties of graphs is the theme of this book. Starting from very elementary regularity properties, the concept of a distance-regular graph arises naturally as a common setting for regular graphs which are extremal in one sense or another. Several other important regular combinatorial structures are then shown to be equivalent to special families of distance-regular graphs. Other subjects of more general interest, such as regularity and extremal properties in graphs, association schemes, representations of graphs in euclidean space, groups and geometries of Lie type, groups acting on graphs, and codes are covered independently. Many new results and proofs and more than 750 references increase the encyclopaedic value of this book.

Author : Zoran Stanić
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110383365
Total Pages : 313 pages
Book Rating : 4.62/5 ( download)

DOWNLOAD NOW!

Download or read book Regular Graphs written by Zoran Stanić and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-04-24 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written for mathematicians working with the theory of graph spectra, this (primarily theoretical) book presents relevant results considering the spectral properties of regular graphs. The book begins with a short introduction including necessary terminology and notation. The author then proceeds with basic properties, specific subclasses of regular graphs (like distance-regular graphs, strongly regular graphs, various designs or expanders) and determining particular regular graphs. Each chapter contains detailed proofs, discussions, comparisons, examples, exercises and also indicates possible applications. Finally, the author also includes some conjectures and open problems to promote further research. Contents Spectral properties Particular types of regular graph Determinations of regular graphs Expanders Distance matrix of regular graphs

Author : Andries E. Brouwer
Publisher :
ISBN 13 : 1316512037
Total Pages : 481 pages
Book Rating : 4.36/5 ( download)

DOWNLOAD NOW!

Download or read book Strongly Regular Graphs written by Andries E. Brouwer and published by . This book was released on 2022-01-13 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph on strongly regular graphs is an invaluable reference for anybody working in algebraic combinatorics.

Author : Chris Godsil
Publisher : Springer Science & Business Media
ISBN 13 : 1461301637
Total Pages : 453 pages
Book Rating : 4.39/5 ( download)

DOWNLOAD NOW!

Download or read book Algebraic Graph Theory written by Chris Godsil and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents and illustrates the main tools and ideas of algebraic graph theory, with a primary emphasis on current rather than classical topics. It is designed to offer self-contained treatment of the topic, with strong emphasis on concrete examples.

Author : Andries E. Brouwer
Publisher : Springer Science & Business Media
ISBN 13 : 1461419395
Total Pages : 254 pages
Book Rating : 4.96/5 ( download)

DOWNLOAD NOW!

Download or read book Spectra of Graphs written by Andries E. Brouwer and published by Springer Science & Business Media. This book was released on 2011-12-17 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics. Exercises at the end of each chapter provide practice and vary from easy yet interesting applications of the treated theory, to little excursions into related topics. Tables, references at the end of the book, an author and subject index enrich the text. Spectra of Graphs is written for researchers, teachers and graduate students interested in graph spectra. The reader is assumed to be familiar with basic linear algebra and eigenvalues, although some more advanced topics in linear algebra, like the Perron-Frobenius theorem and eigenvalue interlacing are included.

Author : Zoran Stanić
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311035134X
Total Pages : 247 pages
Book Rating : 4.47/5 ( download)

DOWNLOAD NOW!

Download or read book Regular Graphs written by Zoran Stanić and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-04-24 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written for mathematicians working with the theory of graph spectra, this (primarily theoretical) book presents relevant results considering the spectral properties of regular graphs. The book begins with a short introduction including necessary terminology and notation. The author then proceeds with basic properties, specific subclasses of regular graphs (like distance-regular graphs, strongly regular graphs, various designs or expanders) and determining particular regular graphs. Each chapter contains detailed proofs, discussions, comparisons, examples, exercises and also indicates possible applications. Finally, the author also includes some conjectures and open problems to promote further research. Contents Spectral properties Particular types of regular graph Determinations of regular graphs Expanders Distance matrix of regular graphs

Author : Benjamin V. C. Collins
Publisher :
ISBN 13 :
Total Pages : 206 pages
Book Rating : 4.21/5 ( download)

DOWNLOAD NOW!

Download or read book Some Problems in the Theory of Distance-regular Graphs written by Benjamin V. C. Collins and published by . This book was released on 1996 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Lowell W. Beineke
Publisher : Cambridge University Press
ISBN 13 : 9780521801973
Total Pages : 302 pages
Book Rating : 4.74/5 ( download)

DOWNLOAD NOW!

Download or read book Topics in Algebraic Graph Theory written by Lowell W. Beineke and published by Cambridge University Press. This book was released on 2004-10-04 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is no other book with such a wide scope of both areas of algebraic graph theory.

Author : Brian Curtin
Publisher :
ISBN 13 :
Total Pages : 322 pages
Book Rating : 4.40/5 ( download)

DOWNLOAD NOW!

Download or read book Bipartite Distance-regular Graphs written by Brian Curtin and published by . This book was released on 1996 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Ravindra B. Bapat
Publisher : Springer
ISBN 13 : 1447165691
Total Pages : 197 pages
Book Rating : 4.99/5 ( download)

DOWNLOAD NOW!

Download or read book Graphs and Matrices written by Ravindra B. Bapat and published by Springer. This book was released on 2014-09-19 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.