D Bounded Distance Regular Graphs

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D Bounded Distance Regular Graphs

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Author : Chih-wen Weng
language : en
Publisher:
Release Date : 1995

D Bounded Distance Regular Graphs written by Chih-wen Weng and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.

Distance Regular Graphs

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Author : Andries E. Brouwer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Distance Regular Graphs written by Andries E. Brouwer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Completely Regular Codes In Distance Regular Graphs

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Author : Minjia Shi
language : en
Publisher: CRC Press
Release Date : 2025-03-14

Completely Regular Codes In Distance Regular Graphs written by Minjia Shi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-14 with Mathematics categories.

The concept of completely regular codes was introduced by Delsarte in his celebrated 1973 thesis, which created the field of Algebraic Combinatorics. This notion was extended by several authors from classical codes over finite fields to codes in distance-regular graphs. Half a century later, there was no book dedicated uniquely to this notion. Most of Delsarte examples were in the Hamming and Johnson graphs. In recent years, many examples were constructed in other distance regular graphs including q-analogues of the previous, and the Doob graph. Completely Regular Codes in Distance Regular Graphs provides, for the first time, a definitive source for the main theoretical notions underpinning this fascinating area of study. It also supplies several useful surveys of constructions using coding theory, design theory and finite geometry in the various families of distance regular graphs of large diameters. Features Written by pioneering experts in the domain Suitable as a research reference at the master’s level Includes extensive tables of completely regular codes in the Hamming graph Features a collection of up-to-date surveys.

Distance Regular Graphs

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Author : Andries E. Brouwer
language : en
Publisher: Springer
Release Date : 2011-12-06

Distance Regular Graphs written by Andries E. Brouwer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-06 with Mathematics categories.

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.

Regular Graphs

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Author : Zoran Stanić
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-04-24

Regular Graphs written by Zoran Stanić and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-24 with Mathematics categories.

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

Strongly Regular Graphs

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Author : Andries E. Brouwer
language : en
Publisher:
Release Date : 2022-01-13

Strongly Regular Graphs written by Andries E. Brouwer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-13 with Language Arts & Disciplines categories.

This monograph on strongly regular graphs is an invaluable reference for anybody working in algebraic combinatorics.

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Author :
language : en
Publisher:
Release Date : 1996

written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.

Algebraic Combinatorics And The Monster Group

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Author : Alexander A. Ivanov
language : en
Publisher: Cambridge University Press
Release Date : 2023-08-17

Algebraic Combinatorics And The Monster Group written by Alexander A. Ivanov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-17 with Mathematics categories.

The current state of knowledge on the Monster group, including Majorana theory, Vertex Operator Algebras, Moonshine and maximal subgroups.

Algebraic Combinatorics

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Author : Chris Godsil
language : en
Publisher: Routledge
Release Date : 2017-10-19

Algebraic Combinatorics written by Chris Godsil and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.

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.

Investigations In Algebraic Theory Of Combinatorial Objects

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Author : I.A. Faradzev
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Investigations In Algebraic Theory Of Combinatorial Objects written by I.A. Faradzev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

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.