Download or read book Graphs and Geometry written by László Lovász and published by American Mathematical Soc.. This book was released on 2019-08-28 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Geometric Graphs and Arrangements written by Stefan Felsner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Thirty Essays on Geometric Graph Theory written by János Pach and published by Springer Science & Business Media. This book was released on 2012-12-15 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Analysis and Geometry on Graphs and Manifolds written by Matthias Keller and published by Cambridge University Press. This book was released on 2020-08-20 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the interplay between several rapidly expanding areas of mathematics. Suitable for graduate students as well as researchers, it provides surveys of topics linking geometry, spectral theory and stochastics.
Download or read book Matrices and Graphs in Geometry written by Miroslav Fiedler and published by Cambridge University Press. This book was released on 2011-02-03 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Demonstrates the close relationship between matrix theory and elementary Euclidean geometry, with emphasis on using simple graph-theoretical notions.
Download or read book Graphs and Geometry written by László Lovász and published by . This book was released on 2019 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Geometry of Cuts and Metrics written by Michel Marie Deza and published by Springer. This book was released on 2009-11-12 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Convexity and Discrete Geometry Including Graph Theory written by Karim Adiprasito and published by Springer. This book was released on 2016-05-02 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents easy-to-understand yet surprising properties obtained using topological, geometric and graph theoretic tools in the areas covered by the Geometry Conference that took place in Mulhouse, France from September 7–11, 2014 in honour of Tudor Zamfirescu on the occasion of his 70th anniversary. The contributions address subjects in convexity and discrete geometry, in distance geometry or with geometrical flavor in combinatorics, graph theory or non-linear analysis. Written by top experts, these papers highlight the close connections between these fields, as well as ties to other domains of geometry and their reciprocal influence. They offer an overview on recent developments in geometry and its border with discrete mathematics, and provide answers to several open questions. The volume addresses a large audience in mathematics, including researchers and graduate students interested in geometry and geometrical problems.
Download or read book Groups Graphs and Trees written by John Meier and published by Cambridge University Press. This book was released on 2008-07-31 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This outstanding new book presents the modern, geometric approach to group theory, in an accessible and engaging approach to the subject. Topics include group actions, the construction of Cayley graphs, and connections to formal language theory and geometry. Theorems are balanced by specific examples such as Baumslag-Solitar groups, the Lamplighter group and Thompson's group. Only exposure to undergraduate-level abstract algebra is presumed, and from that base the core techniques and theorems are developed and recent research is explored. Exercises and figures throughout the text encourage the development of geometric intuition. Ideal for advanced undergraduates looking to deepen their understanding of groups, this book will also be of interest to graduate students and researchers as a gentle introduction to geometric group theory.
Download or read book Beyond Planar Graphs written by Seok-Hee Hong and published by Springer Nature. This book was released on 2020-09-30 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first general and extensive review on the algorithmics and mathematical results of beyond planar graphs. Most real-world data sets are relational and can be modelled as graphs consisting of vertices and edges. Planar graphs are fundamental for both graph theory and graph algorithms and are extensively studied. Structural properties and fundamental algorithms for planar graphs have been discovered. However, most real-world graphs, such as social networks and biological networks, are non-planar. To analyze and visualize such real-world networks, it is necessary to solve fundamental mathematical and algorithmic research questions on sparse non-planar graphs, called beyond planar graphs.This book is based on the National Institute of Informatics (NII) Shonan Meeting on algorithmics on beyond planar graphs held in Japan in November, 2016. The book consists of 13 chapters that represent recent advances in various areas of beyond planar graph research. The main aims and objectives of this book include 1) to timely provide a state-of-the-art survey and a bibliography on beyond planar graphs; 2) to set the research agenda on beyond planar graphs by identifying fundamental research questions and new research directions; and 3) to foster cross-disciplinary research collaboration between computer science (graph drawing and computational geometry) and mathematics (graph theory and combinatorics). New algorithms for beyond planar graphs will be in high demand by practitioners in various application domains to solve complex visualization problems. This book therefore will be a valuable resource for researchers in graph theory, algorithms, and theoretical computer science, and will stimulate further deep scientific investigations into many areas of beyond planar graphs.
Download or read book Random Geometric Graphs written by Mathew Penrose and published by Oxford University Press. This book was released on 2003 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides and explains the mathematics behind geometric graph theory. Applications of this theory are used on the study of neural networks, spread of disease, astrophysics and spatial statistics.
Download or read book Discrete and Computational Geometry Graphs and Games written by Jin Akiyama and published by Springer. This book was released on 2021-10-29 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 21st Japanese Conference on Discrete and Computational Geometry and Graphs, JCDCGGG 2018, held in Quezon City, Philippines, in September 2018. The total of 14 papers included in this volume was carefully reviewed and selected from 25 submissions. The papers feature advances made in the field of computational geometry and focus on emerging technologies, new methodology and applications, graph theory and dynamics.
Download or read book Introduction to Graph Theory written by Richard J. Trudeau and published by Courier Corporation. This book was released on 2013-04-15 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at "the mathematically traumatized," this text offers nontechnical coverage of graph theory, with exercises. Discusses planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. 1976 edition.
Download or read book Combinatorial Geometry written by János Pach and published by John Wiley & Sons. This book was released on 2011-10-18 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete, self-contained introduction to a powerful and resurgingmathematical discipline . Combinatorial Geometry presents andexplains with complete proofs some of the most important resultsand methods of this relatively young mathematical discipline,started by Minkowski, Fejes Toth, Rogers, and Erd???s. Nearly halfthe results presented in this book were discovered over the pasttwenty years, and most have never before appeared in any monograph.Combinatorial Geometry will be of particular interest tomathematicians, computer scientists, physicists, and materialsscientists interested in computational geometry, robotics, sceneanalysis, and computer-aided design. It is also a superb textbook,complete with end-of-chapter problems and hints to their solutionsthat help students clarify their understanding and test theirmastery of the material. Topics covered include: * Geometric number theory * Packing and covering with congruent convex disks * Extremal graph and hypergraph theory * Distribution of distances among finitely many points * Epsilon-nets and Vapnik--Chervonenkis dimension * Geometric graph theory * Geometric discrepancy theory * And much more
Download or read book IPython Interactive Computing and Visualization Cookbook written by Cyrille Rossant and published by Packt Publishing Ltd. This book was released on 2014-09-25 with total page 899 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended to anyone interested in numerical computing and data science: students, researchers, teachers, engineers, analysts, hobbyists... Basic knowledge of Python/NumPy is recommended. Some skills in mathematics will help you understand the theory behind the computational methods.
Download or read book Functions and Graphs written by I. M. Gelfand and published by Courier Corporation. This book was released on 2002-01-01 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents students with problems and exercises designed to illuminate the properties of functions and graphs. The 1st part of the book employs simple functions to analyze the fundamental methods of constructing graphs. The 2nd half deals with more complicated and refined questions concerning linear functions, quadratic trinomials, linear fractional functions, power functions, and rational functions. 1969 edition.
Download or read book A Seminar on Graph Theory written by Frank Harary and published by Courier Dover Publications. This book was released on 2015-07-15 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lectures given in F. Harary's seminar course, University College of London, Dept. of Mathematics, 1962-1963.
