Graph Polynomials
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Graph Polynomials
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Author : Yongtang Shi
language : en
Publisher: CRC Press
Release Date : 2016-11-25
Graph Polynomials written by Yongtang 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 2016-11-25 with Mathematics categories.
This book covers both theoretical and practical results for graph polynomials. Graph polynomials have been developed for measuring combinatorial graph invariants and for characterizing graphs. Various problems in pure and applied graph theory or discrete mathematics can be treated and solved efficiently by using graph polynomials. Graph polynomials have been proven useful areas such as discrete mathematics, engineering, information sciences, mathematical chemistry and related disciplines.
Graphs On Surfaces
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Author : Joanna A. Ellis-Monaghan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-28
Graphs On Surfaces written by Joanna A. Ellis-Monaghan 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 2013-06-28 with Mathematics categories.
Graphs on Surfaces: Dualities, Polynomials, and Knots offers an accessible and comprehensive treatment of recent developments on generalized duals of graphs on surfaces, and their applications. The authors illustrate the interdependency between duality, medial graphs and knots; how this interdependency is reflected in algebraic invariants of graphs and knots; and how it can be exploited to solve problems in graph and knot theory. Taking a constructive approach, the authors emphasize how generalized duals and related ideas arise by localizing classical constructions, such as geometric duals and Tait graphs, and then removing artificial restrictions in these constructions to obtain full extensions of them to embedded graphs. The authors demonstrate the benefits of these generalizations to embedded graphs in chapters describing their applications to graph polynomials and knots. Graphs on Surfaces: Dualities, Polynomials, and Knots also provides a self-contained introduction to graphs on surfaces, generalized duals, topological graph polynomials, and knot polynomials that is accessible both to graph theorists and to knot theorists. Directed at those with some familiarity with basic graph theory and knot theory, this book is appropriate for graduate students and researchers in either area. Because the area is advancing so rapidly, the authors give a comprehensive overview of the topic and include a robust bibliography, aiming to provide the reader with the necessary foundations to stay abreast of the field. The reader will come away from the text convinced of advantages of considering these higher genus analogues of constructions of plane and abstract graphs, and with a good understanding of how they arise.
Chromatic Polynomials And Chromaticity Of Graphs
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Author : F. M. Dong
language : en
Publisher: World Scientific
Release Date : 2005
Chromatic Polynomials And Chromaticity Of Graphs written by F. M. Dong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
"This is the first book to comprehensively cover chromatic polynomials of graphs. It includes most of the known results and unsolved problems in the area of chromatic polynomials. Dividing the book into three main parts, the authors take readers from the rudiments of chromatic polynomials to more complex topics: the chromatic equivalence classes of graphs and the zeros and inequalities of chromatic polynomials. The early material is well suited to a graduate level course while the latter parts will be an invaluable resource for postgraduate students and researchers in combinatorics and graph theory."--BOOK JACKET.
Handbook Of The Tutte Polynomial And Related Topics
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Author : Joanna A. Ellis-Monaghan
language : en
Publisher: CRC Press
Release Date : 2022-07-06
Handbook Of The Tutte Polynomial And Related Topics written by Joanna A. Ellis-Monaghan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-06 with Computers categories.
The Tutte Polynomial touches on nearly every area of combinatorics as well as many other fields, including statistical mechanics, coding theory, and DNA sequencing. It is one of the most studied graph polynomials. Handbook of the Tutte Polynomial and Related Topics is the first handbook published on the Tutte Polynomial. It consists of thirty-four chapters written by experts in the field, which collectively offer a concise overview of the polynomial’s many properties and applications. Each chapter covers a different aspect of the Tutte polynomial and contains the central results and references for its topic. The chapters are organized into six parts. Part I describes the fundamental properties of the Tutte polynomial, providing an overview of the Tutte polynomial and the necessary background for the rest of the handbook. Part II is concerned with questions of computation, complexity, and approximation for the Tutte polynomial; Part III covers a selection of related graph polynomials; Part IV discusses a range of applications of the Tutte polynomial to mathematics, physics, and biology; Part V includes various extensions and generalizations of the Tutte polynomial; and Part VI provides a history of the development of the Tutte polynomial. Features Written in an accessible style for non-experts, yet extensive enough for experts Serves as a comprehensive and accessible introduction to the theory of graph polynomials for researchers in mathematics, physics, and computer science Provides an extensive reference volume for the evaluations, theorems, and properties of the Tutte polynomial and related graph, matroid, and knot invariants Offers broad coverage, touching on the wide range of applications of the Tutte polynomial and its various specializations
Graph Polynomials
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Author : Yongtang Shi
language : en
Publisher: CRC Press
Release Date : 2016-11-25
Graph Polynomials written by Yongtang 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 2016-11-25 with Mathematics categories.
This book covers both theoretical and practical results for graph polynomials. Graph polynomials have been developed for measuring combinatorial graph invariants and for characterizing graphs. Various problems in pure and applied graph theory or discrete mathematics can be treated and solved efficiently by using graph polynomials. Graph polynomials have been proven useful areas such as discrete mathematics, engineering, information sciences, mathematical chemistry and related disciplines.
Algebraic Elements Of Graphs
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Author : Yanpei Liu
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-09-11
Algebraic Elements Of Graphs written by Yanpei Liu 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 2017-09-11 with Mathematics categories.
This book studies algebraic representations of graphs in order to investigate combinatorial structures via local symmetries. Topological, combinatorial and algebraic classifications are distinguished by invariants of polynomial type and algorithms are designed to determine all such classifications with complexity analysis. Being a summary of the author‘s original work on graph embeddings, this book is an essential reference for researchers in graph theory. Contents Abstract Graphs Abstract Maps Duality Orientability Orientable Maps Nonorientable Maps Isomorphisms of Maps Asymmetrization Asymmetrized Petal Bundles Asymmetrized Maps Maps within Symmetry Genus Polynomials Census with Partitions Equations with Partitions Upper Maps of a Graph Genera of a Graph Isogemial Graphs Surface Embeddability
Graph Colouring And Applications
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Author : Pierre Hansen
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Graph Colouring And Applications written by Pierre Hansen 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 1999 with Mathematics categories.
This volume presents the proceedings of the CRM workshop on graph coloring and applications. The articles span a wide spectrum of topics related to graph coloring, including: list-colorings, total colorings, colorings and embeddings of graphs, chromatic polynomials, characteristic polynomials, chromatic scheduling, and graph coloring problems related to frequency assignment. Outstanding researchers in combinatorial optimization and graph theory contributed their work. A list of open problems is included.
Graph Theoretic Concepts In Computer Science
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Author : Christophe Paul
language : en
Publisher: Springer
Release Date : 2009-12-03
Graph Theoretic Concepts In Computer Science written by Christophe Paul and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-03 with Computers categories.
The 35th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2009) took place at Montpellier (France), June 24–26 2009. About 80 computer scientists from all over the world (Australia, Belgium, Canada, China, Czech Republic, France, Germany, Greece, Israel, Japan, Korea, The Netherlands, Norway, Spain, UK, USA) attended the conference. Since1975,ithastakenplace20timesinGermany,fourtimesinTheNeth- lands, twice in Austria, as well as once in Italy, Slovakia, Switzerland, the Czech Republic, France, Norway, and the UK. The conference aims at uniting theory and practice by demonstrating how graph-theoretic concepts can be applied to various areas in computer science, or by extracting new problems from appli- tions. The goal is to present recent research results and to identify and explore directions of future research. The conference is well-balanced with respect to established researchers and young scientists. There were 69 submissions. Each submission was reviewed by at least three, and on average four, Program Committee members. The Committee decided to accept 28 papers. Due to the competition and the limited schedule, some good papers could not be accepted. Theprogramalsoincludedexcellentinvitedtalks:onegivenbyDanielKràlon “AlgorithmsforClassesofGraphswithBoundedExpansion,” the otherbyDavid Eppsteinon“Graph-TheoreticSolutionstoComputationalGeometryProblems.” The proceedings contains two survey papers on these topics.
Logical Approaches To Computational Barriers
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Author : Arnold Beckmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-26
Logical Approaches To Computational Barriers written by Arnold Beckmann 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 2006-06-26 with Computers categories.
This book constitutes the refereed proceedings of the Second International Conference on Computability in Europe, CiE 2006, held in Swansea, UK, June/July 2006. The book presents 31 revised full papers together with 30 invited papers, including papers corresponding to 8 plenary talks and 6 special sessions on proofs and computation, computable analysis, challenges in complexity, foundations of programming, mathematical models of computers and hypercomputers, and Gödel centenary: Gödel's legacy for computability.
Recent Results In The Theory Of Graph Spectra
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Author : D.M. Cvetkovic
language : en
Publisher: Elsevier
Release Date : 1988-01-01
Recent Results In The Theory Of Graph Spectra written by D.M. Cvetkovic and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Mathematics categories.
The purpose of this volume is to review the results in spectral graph theory which have appeared since 1978. The problem of characterizing graphs with least eigenvalue -2 was one of the original problems of spectral graph theory. The techniques used in the investigation of this problem have continued to be useful in other contexts including forbidden subgraph techniques as well as geometric methods involving root systems. In the meantime, the particular problem giving rise to these methods has been solved almost completely. This is indicated in Chapter 1. The study of various combinatorial objects (including distance regular and distance transitive graphs, association schemes, and block designs) have made use of eigenvalue techniques, usually as a method to show the nonexistence of objects with certain parameters. The basic method is to construct a graph which contains the structure of the combinatorial object and then to use the properties of the eigenvalues of the graph. Methods of this type are given in Chapter 2. Several topics have been included in Chapter 3, including the relationships between the spectrum and automorphism group of a graph, the graph isomorphism and the graph reconstruction problem, spectra of random graphs, and the Shannon capacity problem. Some graph polynomials related to the characteristic polynomial are described in Chapter 4. These include the matching, distance, and permanental polynomials. Applications of the theory of graph spectra to Chemistry and other branches of science are described from a mathematical viewpoint in Chapter 5. The last chapter is devoted to the extension of the theory of graph spectra to infinite graphs.