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Distance Regular Graphs

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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.

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.

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

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.

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.

Algebraic Graph Theory

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Author : Chris Godsil
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

Algebraic Graph Theory written by Chris Godsil 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 2013-12-01 with Mathematics categories.

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.