Search results for: topological-graph-theory

Topological Graph Theory

Author : Jonathan L. Gross
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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.

The Foundations of Topological Graph Theory

Author : C.Paul Bonnington
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This is not a traditional work on topological graph theory. No current graph or voltage graph adorns its pages. Its readers will not compute the genus (orientable or non-orientable) of a single non-planar graph. Their muscles will not flex under the strain of lifting walks from base graphs to derived graphs. What is it, then? It is an attempt to place topological graph theory on a purely combinatorial yet rigorous footing. The vehicle chosen for this purpose is the con cept of a 3-graph, which is a combinatorial generalisation of an imbedding. These properly edge-coloured cubic graphs are used to classify surfaces, to generalise the Jordan curve theorem, and to prove Mac Lane's characterisation of planar graphs. Thus they playa central role in this book, but it is not being suggested that they are necessarily the most effective tool in areas of topological graph theory not dealt with in this volume. Fruitful though 3-graphs have been for our investigations, other jewels must be examined with a different lens. The sole requirement for understanding the logical development in this book is some elementary knowledge of vector spaces over the field Z2 of residue classes modulo 2. Groups are occasionally mentioned, but no expertise in group theory is required. The treatment will be appreciated best, however, by readers acquainted with topology. A modicum of topology is required in order to comprehend much of the motivation we supply for some of the concepts introduced.

Topics in Topological Graph Theory

Author : Lowell W. Beineke
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The use of topological ideas to explore various aspects of graph theory, and vice versa, is a fruitful area of research. There are links with other areas of mathematics, such as design theory and geometry, and increasingly with such areas as computer networks where symmetry is an important feature. Other books cover portions of the material here, but there are no other books with such a wide scope. This book contains fifteen expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory and the topology of surfaces. Each chapter concludes with an extensive list of references.

Graphs of Groups on Surfaces

Author : A.T. White
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The book, suitable as both an introductory reference and as a text book in the rapidly growing field of topological graph theory, models both maps (as in map-coloring problems) and groups by means of graph imbeddings on sufaces. Automorphism groups of both graphs and maps are studied. In addition connections are made to other areas of mathematics, such as hypergraphs, block designs, finite geometries, and finite fields. There are chapters on the emerging subfields of enumerative topological graph theory and random topological graph theory, as well as a chapter on the composition of English church-bell music. The latter is facilitated by imbedding the right graph of the right group on an appropriate surface, with suitable symmetries. Throughout the emphasis is on Cayley maps: imbeddings of Cayley graphs for finite groups as (possibly branched) covering projections of surface imbeddings of loop graphs with one vertex. This is not as restrictive as it might sound; many developments in topological graph theory involve such imbeddings. The approach aims to make all this interconnected material readily accessible to a beginning graduate (or an advanced undergraduate) student, while at the same time providing the research mathematician with a useful reference book in topological graph theory. The focus will be on beautiful connections, both elementary and deep, within mathematics that can best be described by the intuitively pleasing device of imbedding graphs of groups on surfaces.

The Foundations of Topological Graph Theory

Author : C. Paul Bonnington
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Topological Graph Theory

Author : Caryl Ann Chacey
File Size : 81.51 MB
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Topological graph theory II

Author : Bojan Mohar
File Size : 40.20 MB
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Algebraic and Topological Graph Theory

Author : Sandi Klavžar
File Size : 48.60 MB
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Special Issue Algebraic and Topological Graph Theory

Author : Sandi Klavžar
File Size : 41.61 MB
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Topological graph theory

Author : Bojan Mohar
File Size : 60.1 MB
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Special Issue Topological Graph Theory

Author : Bojan Mohar
File Size : 55.73 MB
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Topological Graph Theory

Author : Source Wikipedia
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 36. Chapters: Albertson conjecture, Betti number, Book embedding, Combinatorial map, Conway's thrackle conjecture, Covering space, Crossing number (graph theory), Cycle double cover, Dessin d'enfant, Dual graph, Euler characteristic, Fary's theorem, Fork (topology), Fraysseix-Rosenstiehl's planarity criterion, Generalized map, Genus (mathematics), Graph drawing, Graph embedding, Heawood conjecture, Heawood number, Linkless embedding, Regular map (graph theory), Road coloring problem, Rotation system, String graph, Toroidal graph, Water, gas, and electricity.

Computational Results in Topological Graph Theory

Author : John Frederick Pearson
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Graph Theory and Topology in Chemistry

Author : R. Bruce King
File Size : 63.20 MB
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Participants from ten different countries attended the conference which was in many ways a sequel to a symposium held at the University of Georgia in April 1983. The principal goal of this Conference was to provide a forum for chemists and mathematicians to interact and become better informed on current activities and new developments in the broad areas of chemical topology and chemical graph theory. It is intended that this proceedings volume will make available to a wider audience a permanent record of the papers presented at the Conference. The 41 papers span a wide range of topics, and have been grouped into five major sections

Topological Graph Theory

Author : Catharine Wright
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Topics in Structural Graph Theory

Author : Lowell W. Beineke
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The rapidly expanding area of structural graph theory uses ideas of connectivity to explore various aspects of graph theory and vice versa. It has links with other areas of mathematics, such as design theory and is increasingly used in such areas as computer networks where connectivity algorithms are an important feature. Although other books cover parts of this material, none has a similarly wide scope. Ortrud R. Oellermann (Winnipeg), internationally recognised for her substantial contributions to structural graph theory, acted as academic consultant for this volume, helping shape its coverage of key topics. The result is a collection of thirteen expository chapters, each written by acknowledged experts. These contributions have been carefully edited to enhance readability and to standardise the chapter structure, terminology and notation throughout. An introductory chapter details the background material in graph theory and network flows and each chapter concludes with an extensive list of references.

Proceedings of the 10th Workshop on Topological Graph Theory at Yokohama

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Topics in Algebraic Graph Theory

Author : Lowell W. Beineke
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There is no other book with such a wide scope of both areas of algebraic graph theory.

A Theorem from Topological Graph Theory

Author : Leong Weng Ng
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Applications of Graph Theory and Topology in Inorganic Cluster and Coordination Chemistry

Author : R. Bruce King
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Applications of Graph Theory and Topology in Inorganic Cluster and Coordination Chemistry is a text-reference that provides inorganic chemists with a rudimentary knowledge of topology, graph theory, and related mathematical disciplines. The book emphasizes the application of these topics to metal clusters and coordination compounds. The book's initial chapters present background information in topology, graph theory, and group theory, explaining how these topics relate to the properties of atomic orbitals and are applied to coordination polyhedra. Subsequent chapters apply these ideas to the structure and chemical bonding in diverse types of inorganic compounds, including boron cages, metal clusters, solid state materials, metal oxide derivatives, superconductors, icosahedral phases, and carbon cages (fullerenes). The book's final chapter introduces the application of topology and graph theory for studying the dynamics of rearrangements in coordination and cluster polyhedra.