Automorphism Decompositions Of Graphs
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Automorphism Decompositions Of Graphs
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Author : Cara M. Wiblemo
language : en
Publisher:
Release Date : 2010
Automorphism Decompositions Of Graphs written by Cara M. Wiblemo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Automorphisms categories.
A graph has an automorphism decomposition if its adjacency matrix can be written as the sum of permutation matrices, each of which is an automorphism of the graph. These graphs appear to be closely related to Cayley graphs. This paper investigates the properties of graphs with automorphism decompositions. Each must be k-regular, and each edge in such a graph must be in at least (k-2) 4-cycles. We show that graphs that are isomorphic to Cayley graphs on abelian groups always have automorphism decompositions, and all 3-regular graphs with automorphism decompositions are Cayley graphs on abelian groups. Additionally, we investigate the connection to covering graphs.
Characterizations And Properties Of Graphs With Automorphism Decompositions
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Author : Cara M. Wiblemo
language : en
Publisher:
Release Date : 2014
Characterizations And Properties Of Graphs With Automorphism Decompositions written by Cara M. Wiblemo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Automorphisms categories.
This thesis initiates the study of automorphism decompositions of graphs. A connected graph has an automorphism decomposition if its adjacency matrix can be written as the sum of permutation matrices, each of which corresponds to an automorphism of the graph. Quasiabelian Cayley graphs are an example, though there are vertex-transitive non-Cayley graphs with automorphism decompositions as well. Graphs with automorphism decompositions are vertex-transitive, and therefore isomorphic to coset graphs. We prove necessary and sufficient conditions for a coset graph to have an automorphism decomposition given by its connection set. We have results concerning the existence of automorphism decompositions for vertex-transitive non-Cayley graphs of order 28 and below, and partial results for order 30. We also establish upper bounds on the size of the vertex set for a graph with an inverse-closed automorphism decomposition consisting of elements that all have the same order, for orders 2, 3, and 4.
Decompositions Of Graphs
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Author : Juraj Bosák
language : en
Publisher: Taylor & Francis US
Release Date : 1990
Decompositions Of Graphs written by Juraj Bosák and has been published by Taylor & Francis US this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
The Theory Of 2 Structures
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Author : Andrzej Ehrenfeucht
language : en
Publisher: World Scientific
Release Date : 1999
The Theory Of 2 Structures written by Andrzej Ehrenfeucht and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 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 theoretical 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.
The Theory Of 2 Structures
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Author : A Ehrenfeucht
language : en
Publisher: World Scientific Publishing Company
Release Date : 1999-08-30
The Theory Of 2 Structures written by A 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. Request Inspection Copy
Graph Decompositions With A Sharply Vertex Transitive Automorphism Group
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Author : Anita Pasotti
language : en
Publisher:
Release Date : 2006
Graph Decompositions With A Sharply Vertex Transitive Automorphism Group written by Anita Pasotti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Topics In Graph Automorphisms And Reconstruction
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Author : Josef Lauri
language : en
Publisher: Cambridge University Press
Release Date : 2016-06-02
Topics In Graph Automorphisms And Reconstruction written by Josef Lauri 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 2016-06-02 with Mathematics categories.
An in-depth coverage of selected areas of graph theory focusing on symmetry properties of graphs, ideal for beginners and specialists.
The Classification Of Minimal Graphs With Given Abelian Automorphism Group
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Author : William C. Arlinghaus
language : en
Publisher: American Mathematical Soc.
Release Date : 1985
The Classification Of Minimal Graphs With Given Abelian Automorphism Group written by William C. Arlinghaus 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 1985 with Mathematics categories.
Any finite abstract group can be realized as the automorphism group of a graph. The purpose of this memoir is to find the realization, for each finite abelian group, with the least number of vertices possible. The results are extended to all finite abelian groups. Thus a complete classification is provided for minimal graphs with given finite abelian automorphism group.
Topological Graph Theory
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Author : Jonathan L. Gross
language : en
Publisher: Courier Corporation
Release Date : 2001-01-01
Topological Graph Theory written by Jonathan L. Gross and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.
Iintroductory treatment emphasizes graph imbedding but also covers connections between topological graph theory and other areas of mathematics. Authors explore the role of voltage graphs in the derivation of genus formulas, explain the Ringel-Youngs theorem, and examine the genus of a group, including imbeddings of Cayley graphs. Many figures. 1987 edition.
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.