Graphs And Geometry
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Graphs And Geometry
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Author : László Lovász
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-08-28
Graphs And Geometry written by László Lovász and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-28 with Geometry categories.
Graphs are usually represented as geometric objects drawn in the plane, consisting of nodes and curves connecting them. The main message of this book is that such a representation is not merely a way to visualize the graph, but an important mathematical tool. It is obvious that this geometry is crucial in engineering, for example, if you want to understand rigidity of frameworks and mobility of mechanisms. But even if there is no geometry directly connected to the graph-theoretic problem, a well-chosen geometric embedding has mathematical meaning and applications in proofs and algorithms. This book surveys a number of such connections between graph theory and geometry: among others, rubber band representations, coin representations, orthogonal representations, and discrete analytic functions. Applications are given in information theory, statistical physics, graph algorithms and quantum physics. The book is based on courses and lectures that the author has given over the last few decades and offers readers with some knowledge of graph theory, linear algebra, and probability a thorough introduction to this exciting new area with a large collection of illuminating examples and exercises.
Matrices And Graphs In Geometry
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Author : Miroslav Fiedler
language : en
Publisher: Cambridge University Press
Release Date : 2011-02-03
Matrices And Graphs In Geometry written by Miroslav Fiedler 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 2011-02-03 with Mathematics categories.
Demonstrates the close relationship between matrix theory and elementary Euclidean geometry, with emphasis on using simple graph-theoretical notions.
Geometric Graphs And Arrangements
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Author : Stefan Felsner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Graphs And Arrangements written by Stefan Felsner 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.
Among the intuitively appealing aspects of graph theory is its close connection to drawings and geometry. The development of computer technology has become a source of motivation to reconsider these connections, in particular geometric graphs are emerging as a new subfield of graph theory. Arrangements of points and lines are the objects for many challenging problems and surprising solutions in combinatorial geometry. The book is a collection of beautiful and partly very recent results from the intersection of geometry, graph theory and combinatorics.
Thirty Essays On Geometric Graph Theory
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Author : János Pach
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-15
Thirty Essays On Geometric Graph Theory written by János Pach 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 2012-12-15 with Mathematics categories.
In many applications of graph theory, graphs are regarded as geometric objects drawn in the plane or in some other surface. The traditional methods of "abstract" graph theory are often incapable of providing satisfactory answers to questions arising in such applications. In the past couple of decades, many powerful new combinatorial and topological techniques have been developed to tackle these problems. Today geometric graph theory is a burgeoning field with many striking results and appealing open questions. This contributed volume contains thirty original survey and research papers on important recent developments in geometric graph theory. The contributions were thoroughly reviewed and written by excellent researchers in this field.
Random Graphs Geometry And Asymptotic Structure
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Author : Michael Krivelevich
language : en
Publisher: Cambridge University Press
Release Date : 2016-04-25
Random Graphs Geometry And Asymptotic Structure written by Michael Krivelevich 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 2016-04-25 with Mathematics categories.
A concise introduction, aimed at young researchers, to recent developments of a geometric and topological nature in random graphs.
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.
Geometry Of Cuts And Metrics
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Author : Michel Marie Deza
language : en
Publisher: Springer
Release Date : 2009-11-12
Geometry Of Cuts And Metrics written by Michel Marie Deza and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-12 with Mathematics categories.
Cuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, combinatorial matrix theory, statistical physics, VLSI design etc. This book presents a wealth of results, from different mathematical disciplines, in a unified comprehensive manner, and establishes new and old links, which cannot be found elsewhere. It provides a unique and invaluable source for researchers and graduate students. From the Reviews: "This book is definitely a milestone in the literature of integer programming and combinatorial optimization. It draws from the Interdisciplinarity of these fields [...]. With knowledge about the relevant terms, one can enjoy special subsections without being entirely familiar with the rest of the chapter. This makes it not only an interesting research book but even a dictionary. [...] The longer one works with it, the more beautiful it becomes." Optima 56, 1997.
Computational Geometry Graphs And Applications
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Author : Jin Akiyama
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-26
Computational Geometry Graphs And Applications written by Jin Akiyama 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 2011-10-26 with Computers categories.
This book constitutes the thoroughly refereed post-conference proceedings of the China-Japan Joint Conference on Computational Geometry, Graphs and Applications, CGGA 2010, held in Dalian, China, in November 2010. The 23 revised full papers presented were carefully selected during two rounds of reviewing and improvement from numerous submissions. All aspects of computational and discrete geometry, graph theory, graph algorithms, and their applications are covered.
Geometry Structure And Randomness In Combinatorics
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Author : Jiří Matousek
language : en
Publisher: Springer
Release Date : 2015-04-09
Geometry Structure And Randomness In Combinatorics written by Jiří Matousek and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-09 with Mathematics categories.
This book collects some surveys on current trends in discrete mathematics and discrete geometry. The areas covered include: graph representations, structural graphs theory, extremal graph theory, Ramsey theory and constrained satisfaction problems.
Analysis And Geometry On Graphs And Manifolds
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Author : Matthias Keller
language : en
Publisher: Cambridge University Press
Release Date : 2020-08-20
Analysis And Geometry On Graphs And Manifolds written by Matthias Keller 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 2020-08-20 with Mathematics categories.
A contemporary exploration of the interplay between geometry, spectral theory and stochastics which is explored for graphs and manifolds.