Graphs and geometry

by Lovász, László

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Title Statements

Full title :Graphs and geometry / László Lovász

Summary

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

Edition Statements

Publication Date:©2019

Publication Statements

Publisher(s):American mathematical Society
Place of Publication:Providence, Rhode Island
Language:eng
Publication Date:©2019

The Physical Object

Description:1 online resource (x, 444 pages) : : illustrations

Edition Identifiers

ISBN:9781470453541, 1470453541
oclc:on1117631897
LC Classification:QA90
Dewey Decimal:511/.5

Why are geometric representations interesting? -- Planar graphs -- Rubber bands -- Discrete harmonic functions -- Coin representation -- Square tilings -- Discrete analytic functions -- Discrete analytic functions: Statistical physics -- Adjacency matrix and its square -- Orthogonal representations: Dimension -- Orthogonal representations: The smallest cone -- Orthogonal representations: Quantum physics -- Semidefinite optimization -- Stresses -- Rigidity and motions of frameworks -- The Colin de Verdière number -- Metric representations -- Matching and covering in frameworks -- Combinatorics of subspaces.

Subjects

Combinatorics & graph theory Electronic books Geometrie Géométrie -- Méthodes graphiques geometry Geometry -- Graphic methods Graph theory MATHEMATICS -- Graphic Methods Mathématiques -- Méthodes graphiques Représentations de graphes Representations of graphs