D-bounded Distance-regular Graphs
Author : Chih-wen Weng
Publisher :
Page : 222 pages
File Size : 37,71 MB
Release : 1995
Category :
ISBN :
Distance-Regular Graphs
Author : Andries E. Brouwer
Publisher : Springer Science & Business Media
Page : 513 pages
File Size : 46,42 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3642743412
Book Description
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
Author : Andries E. Brouwer
Publisher :
Page : 481 pages
File Size : 39,96 MB
Release : 2022-01-13
Category : Language Arts & Disciplines
ISBN : 1316512037
Book Description
This monograph on strongly regular graphs is an invaluable reference for anybody working in algebraic combinatorics.
Regular Graphs
Author : Zoran Stanić
Publisher : Walter de Gruyter GmbH & Co KG
Page : 247 pages
File Size : 45,92 MB
Release : 2017-04-24
Category : Mathematics
ISBN : 311035134X
Book Description
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 Combinatorics and the Monster Group
Author : Alexander A. Ivanov
Publisher : Cambridge University Press
Page : 583 pages
File Size : 18,37 MB
Release : 2023-08-17
Category : Mathematics
ISBN : 1009338048
Book Description
The current state of knowledge on the Monster group, including Majorana theory, Vertex Operator Algebras, Moonshine and maximal subgroups.
Algebraic Combinatorics
Author : Chris Godsil
Publisher : Routledge
Page : 382 pages
File Size : 42,52 MB
Release : 2017-10-19
Category : Mathematics
ISBN : 1351467506
Book Description
This graduate level text is distinguished both by the range of topics and the novelty of the material it treats--more than half of the material in it has previously only appeared in research papers. The first half of this book introduces the characteristic and matchings polynomials of a graph. It is instructive to consider these polynomials together because they have a number of properties in common. The matchings polynomial has links with a number of problems in combinatorial enumeration, particularly some of the current work on the combinatorics of orthogonal polynomials. This connection is discussed at some length, and is also in part the stimulus for the inclusion of chapters on orthogonal polynomials and formal power series. Many of the properties of orthogonal polynomials are derived from properties of characteristic polynomials. The second half of the book introduces the theory of polynomial spaces, which provide easy access to a number of important results in design theory, coding theory and the theory of association schemes. This book should be of interest to second year graduate text/reference in mathematics.
Finite Generalized Quadrangles
Author : Stanley E. Payne
Publisher : European Mathematical Society
Page : 304 pages
File Size : 24,56 MB
Release : 2009
Category : Mathematics
ISBN : 9783037190661
Book Description
Generalized quadrangles (GQ) were formally introduced by J. Tits in 1959 to describe geometric properties of simple groups of Lie type of rank 2. The first edition of Finite Generalized Quadrangles (FGQ) quickly became the standard reference for finite GQ. The second edition is essentially a reprint of the first edition. It is a careful rendering into LaTeX of the original, along with an appendix that brings to the attention of the reader those major new results pertaining to GQ, especially in those areas where the authors of this work have made a contribution. The first edition has been out of print for many years. The new edition makes available again this classical reference in the rapidly increasing field of finite geometries.
数理科学講究錄
Author :
Publisher :
Page : 532 pages
File Size : 21,83 MB
Release : 1996
Category : Mathematics
ISBN :
Book Description
Investigations in Algebraic Theory of Combinatorial Objects
Author : I.A. Faradzev
Publisher : Springer Science & Business Media
Page : 513 pages
File Size : 34,72 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 9401719721
Book Description
X Köchendorffer, L.A. Kalu:lnin and their students in the 50s and 60s. Nowadays the most deeply developed is the theory of binary invariant relations and their combinatorial approximations. These combinatorial approximations arose repeatedly during this century under various names (Hecke algebras, centralizer rings, association schemes, coherent configurations, cellular rings, etc.-see the first paper of the collection for details) andin various branches of mathematics, both pure and applied. One of these approximations, the theory of cellular rings (cellular algebras), was developed at the end of the 60s by B. Yu. Weisfeiler and A.A. Leman in the course of the first serious attempt to study the complexity of the graph isomorphism problem, one of the central problems in the modern theory of combinatorial algorithms. At roughly the same time G.M. Adelson-Velskir, V.L. Arlazarov, I.A. Faradtev and their colleagues had developed a rather efficient tool for the constructive enumeration of combinatorial objects based on the branch and bound method. By means of this tool a number of "sports-like" results were obtained. Some of these results are still unsurpassed.
Codes on Euclidean Spheres
Author : T. Ericson
Publisher : Elsevier
Page : 565 pages
File Size : 50,83 MB
Release : 2001-04-27
Category : Mathematics
ISBN : 0080502164
Book Description
Codes on Euclidean spheres are often referred to as spherical codes. They are of interest from mathematical, physical and engineering points of view. Mathematically the topic belongs to the realm of algebraic combinatorics, with close connections to number theory, geometry, combinatorial theory, and - of course - to algebraic coding theory. The connections to physics occur within areas like crystallography and nuclear physics. In engineering spherical codes are of central importance in connection with error-control in communication systems. In that context the use of spherical codes is often referred to as "coded modulation." The book offers a first complete treatment of the mathematical theory of codes on Euclidean spheres. Many new results are published here for the first time. Engineering applications are emphasized throughout the text. The theory is illustrated by many examples. The book also contains an extensive table of best known spherical codes in dimensions 3-24, including exact constructions.
