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.
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.
Cycles And Rays
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Author : Gena Hahn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Cycles And Rays written by Gena Hahn 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 2012-12-06 with Mathematics categories.
What is the "archetypal" image that comes to mind when one thinks of an infinite graph? What with a finite graph - when it is thought of as opposed to an infinite one? What structural elements are typical for either - by their presence or absence - yet provide a common ground for both? In planning the workshop on "Cycles and Rays" it had been intended from the outset to bring infinite graphs to the fore as much as possible. There never had been a graph theoretical meeting in which infinite graphs were more than "also rans", let alone one in which they were a central theme. In part, this is a matter of fashion, inasmuch as they are perceived as not readily lending themselves to applications, in part it is a matter of psychology stemming from the insecurity that many graph theorists feel in the face of set theory - on which infinite graph theory relies to a considerable extent. The result is that by and large, infinite graph theorists know what is happening in finite graphs but not conversely. Lack of knowledge about infinite graph theory can also be found in authoritative l sources. For example, a recent edition (1987) of a major mathematical encyclopaedia proposes to ". . . restrict [itself] to finite graphs, since only they give a typical theory". If anything, the reverse is true, and needless to say, the graph theoretical world knows better. One may wonder, however, by how much.
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.
Directions In Infinite Graph Theory And Combinatorics
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Author : R. Diestel
language : en
Publisher: Elsevier
Release Date : 2016-06-06
Directions In Infinite Graph Theory And Combinatorics written by R. Diestel and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-06 with Mathematics categories.
This book has arisen from a colloquium held at St. John's College, Cambridge, in July 1989, which brought together most of today's leading experts in the field of infinite graph theory and combinatorics. This was the first such meeting ever held, and its aim was to assess the state of the art in the discipline, to consider its links with other parts of mathematics, and to discuss possible directions for future development. This volume reflects the Cambridge meeting in both level and scope. It contains research papers as well as expository surveys of particular areas. Together they offer a comprehensive portrait of infinite graph theory and combinatorics, which should be particularly attractive to anyone new to the discipline.
Handbook Of Graph Theory
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Author : Jonathan L. Gross
language : en
Publisher: CRC Press
Release Date : 2013-12-17
Handbook Of Graph Theory written by Jonathan L. Gross and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-17 with Computers categories.
In the ten years since the publication of the best-selling first edition, more than 1,000 graph theory papers have been published each year. Reflecting these advances, Handbook of Graph Theory, Second Edition provides comprehensive coverage of the main topics in pure and applied graph theory. This second edition-over 400 pages longer than its prede
Decompositions Of Graphs
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Author : Juraj Bosák
language : en
Publisher: Springer
Release Date : 1990-08-31
Decompositions Of Graphs written by Juraj Bosák and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-08-31 with Mathematics categories.
This nice text (twenty years in the writing, published posthumously) would serve well to introduce graduate students (those who can afford it ) to a rich and important class of graph-theoretic problems and concepts. Fifteen short chapters (under three broad topical heads), to each of which are attac
Graph Decompositions
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Author : Reinhard Diestel
language : en
Publisher: Oxford Science Publications
Release Date : 1990
Graph Decompositions written by Reinhard Diestel and has been published by Oxford Science Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Language Arts & Disciplines categories.
Graph Decompositions is the first book on a topic that belongs mainly to infinite graph theory. It offers a complete account of the theory of simplicial decompositions of graphs, from its origins in the 1930s right up to present-day research.In addition to being one of the most important tools in infinite graph theory, simplicial decompositions may be seen as a model for any kind of structural graph decomposition. The currently topical tree-decompositions, for example, have their origin in simplicial decompositions.The text is centred around a few guiding problems and concepts, such as the existence and the uniqueness problem of simplicial decompositions into primes, or the concept of excluded minors as a means of identifying a desired structure.It attempts to give as authentic a picture as possible ofresearch in progress. To this end, it includes discussions of examples, proof strategies on the formation of new concepts, as well as numerous exercises and open problems.Graph Decompositions should prove attractive to any graph theorist or other mathematician interested in a new area of research, as well as to the advanced student looking for a lively and inspiring account of how such research evolves.
Decompositions Packings And Coverings Of Complete Directed Graphs With A 3 Circuit And A Pendent Arc
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Author :
language : en
Publisher:
Release Date : 2007
Decompositions Packings And Coverings Of Complete Directed Graphs With A 3 Circuit And A Pendent Arc written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
In the study of Graph theory, there are eight orientations of the complete graph on three vertices with a pendant edge, K3 [{e}. Two of these are the 3-circuit with a pendant arc and the other six are transitive triples with a pendant arc. Necessary and sufficient conditions are given for decompositions, packings, and coverings of the complete digraph with the two 3-circuit with a pendant arc orientations.
Graph Theory And Decomposition
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Author : Jomon Kottarathil
language : en
Publisher:
Release Date : 2024-04-08
Graph Theory And Decomposition written by Jomon Kottarathil and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-08 with Mathematics categories.
The book Graph Theory and Decomposition covers major areas of the decomposition of graphs. It is a three-part reference book with nine chapters that is aimed at enthusiasts as well as research scholars. It comprehends historical evolution and basic terminologies, and it deliberates on decompositions into cyclic graphs, such as cycle, digraph, and K4-e decompositions. In addition to determining the pendant number of graphs, it has a discourse on decomposing a graph into acyclic graphs like general tree, path, and star decompositions. It summarises another recently developed decomposition technique, which decomposes the given graph into multiple types of subgraphs. Major conjectures on graph decompositions are elaborately discussed. It alludes to a comprehensive bibliography that includes over 500 monographs and journal articles. It includes more than 500 theorems, around 100 definitions, 56 conjectures, 40 open problems, and an algorithm. The index section facilitates easy access to definitions, major conjectures, and named theorems. Thus, the book Graph Theory and Decomposition will be a great asset, we hope, in the field of decompositions of graphs and will serve as a reference book for all who are passionate about graph theory.