Author : Andries E. Brouwer
Publisher :
Page : 481 pages
File Size : 47,45 MB
Release : 2022-01-13
Category : Language Arts & Disciplines
ISBN : 1316512037
This monograph on strongly regular graphs is an invaluable reference for anybody working in algebraic combinatorics.
Author : Andries E. Brouwer
Publisher : Springer Science & Business Media
Page : 513 pages
File Size : 15,77 MB
Release : 2012-12-06
Category : 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.
Author : Josef Lauri
Publisher : Cambridge University Press
Page : 207 pages
File Size : 37,22 MB
Release : 2016-06-02
Category : Mathematics
ISBN : 1316610446
An in-depth coverage of selected areas of graph theory focusing on symmetry properties of graphs, ideal for beginners and specialists.
Author : J. J. Seidel
Publisher : Academic Press
Page : 431 pages
File Size : 13,59 MB
Release : 2014-05-10
Category : Mathematics
ISBN : 1483268004
Geometry and Combinatorics: Selected Works of J. J. Seidel brings together some of the works of J. J. Seidel in geometry and combinatorics. Seidel's selected papers are divided into four areas: graphs and designs; lines with few angles; matrices and forms; and non-Euclidean geometry. A list of all of Seidel's publications is included. Comprised of 29 chapters, this book begins with a discussion on equilateral point sets in elliptic geometry, followed by an analysis of strongly regular graphs of L2-type and of triangular type. The reader is then introduced to strongly regular graphs with (-1, 1, 0) adjacency matrix having eigenvalue 3; graphs related to exceptional root systems; and equiangular lines. Subsequent chapters deal with the regular two-graph on 276 vertices; the congruence order of the elliptic plane; equi-isoclinic subspaces of Euclidean spaces; and Wielandt's visibility theorem. This monograph will be of interest to students and practitioners in the field of mathematics.
Author : Andries E. Brouwer
Publisher : Springer Science & Business Media
Page : 254 pages
File Size : 33,30 MB
Release : 2011-12-17
Category : 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.
Author : Ravindra B. Bapat
Publisher : Springer
Page : 197 pages
File Size : 27,29 MB
Release : 2014-09-19
Category : Mathematics
ISBN : 1447165691
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.
Author : Chris Godsil
Publisher : Springer Science & Business Media
Page : 453 pages
File Size : 29,98 MB
Release : 2013-12-01
Category : Mathematics
ISBN : 1461301637
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 : Akbar Ali
Publisher : Springer Nature
Page : 109 pages
File Size : 21,40 MB
Release : 2021-05-20
Category : Mathematics
ISBN : 3030679934
Die Theorie der regularen Graphen (The Theory of Regular Graphs), written by the Danish Mathematician Julius Petersen in 1891, is often considered the first strictly theoretical paper dealing with graphs. In the 130 years since then, regular graphs have been a common and popular area of study. While regular graphs are typically considered to be graphs whose vertices all have the same degree, a more general interpretation is that of graphs possessing some common characteristic throughout their structure. During the past several decades, however, there has been some increased interest in investigating graphs possessing a property that is, in a sense, opposite to regularity. It is this topic with which this book deals, giving rise to a study of what might be called irregularity in graphs. Here, various irregularity concepts dealing with several topics in graph theory are described, such as degrees of vertices, graph labelings, weightings, colorings, graph structures, Eulerian and Hamiltonian properties, graph decompositions, and Ramsey-type problems.
Author : Thomas W. Cusick
Publisher : Academic Press
Page : 245 pages
File Size : 42,37 MB
Release : 2009-03-04
Category : Mathematics
ISBN : 0080952224
Boolean functions are the building blocks of symmetric cryptographic systems. Symmetrical cryptographic algorithms are fundamental tools in the design of all types of digital security systems (i.e. communications, financial and e-commerce).Cryptographic Boolean Functions and Applications is a concise reference that shows how Boolean functions are used in cryptography. Currently, practitioners who need to apply Boolean functions in the design of cryptographic algorithms and protocols need to patch together needed information from a variety of resources (books, journal articles and other sources). This book compiles the key essential information in one easy to use, step-by-step reference. Beginning with the basics of the necessary theory the book goes on to examine more technical topics, some of which are at the frontier of current research. Serves as a complete resource for the successful design or implementation of cryptographic algorithms or protocols using Boolean functions Provides engineers and scientists with a needed reference for the use of Boolean functions in cryptography Addresses the issues of cryptographic Boolean functions theory and applications in one concentrated resource Organized logically to help the reader easily understand the topic
Author : D. A. Holton
Publisher : Cambridge University Press
Page : 367 pages
File Size : 14,4 MB
Release : 1993-04-22
Category : Mathematics
ISBN : 0521435943
The authors examine various areas of graph theory, using the prominent role of the Petersen graph as a unifying feature.
