Distance-Regular Graphs
Title | Distance-Regular Graphs PDF eBook |
Author | Andries E. Brouwer |
Publisher | Springer Science & Business Media |
Pages | 513 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 3642743412 |
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.
Distance-Regular Graphs
Title | Distance-Regular Graphs PDF eBook |
Author | Andries E. Brouwer |
Publisher | Springer |
Pages | 0 |
Release | 2011-12-06 |
Genre | Mathematics |
ISBN | 9783642743436 |
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.
Strongly Regular Graphs
Title | Strongly Regular Graphs PDF eBook |
Author | Andries E. Brouwer |
Publisher | |
Pages | 481 |
Release | 2022-01-13 |
Genre | Language Arts & Disciplines |
ISBN | 1316512037 |
This monograph on strongly regular graphs is an invaluable reference for anybody working in algebraic combinatorics.
Regular Graphs
Title | Regular Graphs PDF eBook |
Author | Zoran Stanić |
Publisher | Walter de Gruyter GmbH & Co KG |
Pages | 313 |
Release | 2017-04-24 |
Genre | Mathematics |
ISBN | 3110383365 |
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
Algebraic Graph Theory
Title | Algebraic Graph Theory PDF eBook |
Author | Chris Godsil |
Publisher | Springer Science & Business Media |
Pages | 468 |
Release | 2001-04-20 |
Genre | Mathematics |
ISBN | 9780387952208 |
This book is primarily aimed at graduate students and researchers in graph theory, combinatorics, or discrete mathematics in general. However, all the necessary graph theory is developed from scratch, so the only pre-requisite for reading it is a first course in linear algebra and a small amount of elementary group theory. It should be accessible to motivated upper-level undergraduates.
Spectra of Graphs
Title | Spectra of Graphs PDF eBook |
Author | Andries E. Brouwer |
Publisher | Springer Science & Business Media |
Pages | 254 |
Release | 2011-12-17 |
Genre | Mathematics |
ISBN | 1461419395 |
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.
Some Problems in the Theory of Distance-regular Graphs
Title | Some Problems in the Theory of Distance-regular Graphs PDF eBook |
Author | Benjamin V. C. Collins |
Publisher | |
Pages | 206 |
Release | 1996 |
Genre | |
ISBN |