Transitive Decompositions Of Graphs
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Transitive Decompositions Of Graphs
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Author : Geoffrey Pearce
language : en
Publisher:
Release Date : 2007
Transitive Decompositions Of Graphs written by Geoffrey Pearce and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Decomposition (Mathematics) categories.
A transitive decomposition of a graph is a partition of the arc set such that there exists a group of automorphisms of the graph which preserves and acts transitively on the partition. This turns out to be a very broad idea, with several striking connections with other areas of mathematics. In this thesis we first develop some general theory of transitive decompositions, and in particular we illustrate some of the more interesting connections with certain combinatorial and geometric structures. We then give complete, or nearly complete, structural characterisations of certain classes of transitive decompositions preserved by a group with a rank 3 action on vertices (such a group has exactly two orbits on ordered pairs of distinct vertices). The main classes of rank 3 groups we study (namely those which are imprimitive, or primitive of grid type) are derived in some way from 2-transitive groups (that is, groups which are transitive on ordered pairs of distinct vertices), and the results we achieve make use of the classification by Sibley in 2004 of transitive decompositions preserved by a 2-transitive group.
Permutation Groups And Cartesian Decompositions
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Author : Cheryl E. Praeger
language : en
Publisher:
Release Date : 2018-05-03
Permutation Groups And Cartesian Decompositions written by Cheryl E. Praeger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-03 with Mathematics categories.
Concise introduction to permutation groups, focusing on invariant cartesian decompositions and applications in algebra and combinatorics.
Applications Of Group Theory To Combinatorics
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Author : Jack Koolen
language : en
Publisher: CRC Press
Release Date : 2008-07-02
Applications Of Group Theory To Combinatorics written by Jack Koolen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-02 with Mathematics categories.
Applications of Group Theory to Combinatorics contains 11 survey papers from international experts in combinatorics, group theory and combinatorial topology. The contributions cover topics from quite a diverse spectrum, such as design theory, Belyi functions, group theory, transitive graphs, regular maps, and Hurwitz problems, and present the state
Theory Of 2 Structures The A Framework For Decomposition And Transformation Of Graphs
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Author : Andrzej Ehrenfeucht
language : en
Publisher: World Scientific Publishing Company
Release Date : 1999-08-30
Theory Of 2 Structures The A Framework For Decomposition And Transformation Of Graphs written by Andrzej Ehrenfeucht and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-08-30 with Mathematics categories.
The theory of 2-structures provides a convenient framework for decomposition and transformation of mathematical systems where one or several different binary relationships hold between the objects of the system. In particular, it forms a useful framework for decomposition and transformation of graphs.The decomposition methods presented in this book correspond closely to the top-down design methods studied in computer science. The transformation methods considered here have a natural interpretation in the dynamic evolution of certain kinds of communication networks. From the mathematical point of view, the clan decomposition method presented here, also known as modular decomposition or substitution decomposition, is closely related to the decomposition by quotients in algebra. The transformation method presented here is based on labelled 2-structures over groups, the theory of which generalizes the well-studied theory of switching classes of graphs.This book is both a text and a monograph. As a monograph, the results concerning the decomposition and transformation of 2-structures are presented in a unified way. In addition, detailed notes on references are provided at the end of each chapter. These notes allow the reader to trace the origin of many notions and results, and to browse through the literature in order to extend the material presented in the book.To facilitate its use as a textbook, there are numerous examples and exercises which provide an opportunity for the reader to check his or her understanding of the discussed material. Furthermore, the text begins with preliminaries on partial orders, semigroups, groups and graphs to the extent needed for the book.
Handbook Of Graph Theory Combinatorial Optimization And Algorithms
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Author : Krishnaiyan "KT" Thulasiraman
language : en
Publisher: CRC Press
Release Date : 2016-01-05
Handbook Of Graph Theory Combinatorial Optimization And Algorithms written by Krishnaiyan "KT" Thulasiraman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-05 with Computers categories.
The fusion between graph theory and combinatorial optimization has led to theoretically profound and practically useful algorithms, yet there is no book that currently covers both areas together. Handbook of Graph Theory, Combinatorial Optimization, and Algorithms is the first to present a unified, comprehensive treatment of both graph theory and c
Algorithmic Graph Theory And Perfect Graphs
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Author : Martin Charles Golumbic
language : en
Publisher: Elsevier
Release Date : 2014-05-10
Algorithmic Graph Theory And Perfect Graphs written by Martin Charles Golumbic and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Algorithmic Graph Theory and Perfect Graphs provides an introduction to graph theory through practical problems. This book presents the mathematical and algorithmic properties of special classes of perfect graphs. Organized into 12 chapters, this book begins with an overview of the graph theoretic notions and the algorithmic design. This text then examines the complexity analysis of computer algorithm and explains the differences between computability and computational complexity. Other chapters consider the parameters and properties of a perfect graph and explore the class of perfect graphs known as comparability graph or transitively orientable graphs. This book discusses as well the two characterizations of triangulated graphs, one algorithmic and the other graph theoretic. The final chapter deals with the method of performing Gaussian elimination on a sparse matrix wherein an arbitrary choice of pivots may result in the filling of some zero positions with nonzeros. This book is a valuable resource for mathematicians and computer scientists.
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 Drawing And Network Visualization
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Author : Therese Biedl
language : en
Publisher: Springer
Release Date : 2018-12-17
Graph Drawing And Network Visualization written by Therese Biedl and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-17 with Computers categories.
This book constitutes the refereed proceedings of the 26th International Symposium on Graph Drawing and Network Visualization, GD 2018, held in Barcelona, Spain, in September 2018. The 41 full papers presented in this volume were carefully reviewed and selected from 85 submissions. They were organized in topical sections named: planarity variants; upward drawings; RAC drawings; orders; crossings; crossing angles; contact representations; specialized graphs and trees; partially fixed drawings, experiments; orthogonal drawings; realizability; and miscellaneous. The book also contains one invited talk in full paper length and the Graph Drawing contest report.
Journal Of Research Of The National Bureau Of Standards
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Author : United States. National Bureau of Standards
language : en
Publisher:
Release Date : 1988
Journal Of Research Of The National Bureau Of Standards written by United States. National Bureau of Standards and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Chemistry categories.
Irregularity In Graphs
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Author : Akbar Ali
language : en
Publisher: Springer Nature
Release Date : 2021-05-20
Irregularity In Graphs written by Akbar Ali and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-20 with Mathematics categories.
Die Theorie der regularen Graphen (The Theory of Regular Graphs), written by the Danish Mathematician Julius Petersen in 1891, is often considered the first strictly theoretical paper dealing with graphs. In the 130 years since then, regular graphs have been a common and popular area of study. While regular graphs are typically considered to be graphs whose vertices all have the same degree, a more general interpretation is that of graphs possessing some common characteristic throughout their structure. During the past several decades, however, there has been some increased interest in investigating graphs possessing a property that is, in a sense, opposite to regularity. It is this topic with which this book deals, giving rise to a study of what might be called irregularity in graphs. Here, various irregularity concepts dealing with several topics in graph theory are described, such as degrees of vertices, graph labelings, weightings, colorings, graph structures, Eulerian and Hamiltonian properties, graph decompositions, and Ramsey-type problems.