This volume contains the accounts of the principal survey papers presented at GRAPHS and ORDER, held at Banff, Canada from May 18 to May 31, 1984.

Author: Ivan Rival

Publisher: Springer Science & Business Media

ISBN: 9789400953154

Category: Mathematics

Page: 816

View: 992

This volume contains the accounts of the principal survey papers presented at GRAPHS and ORDER, held at Banff, Canada from May 18 to May 31, 1984. This conference was supported by grants from the N.A.T.O. Advanced Study Institute programme, the Natural Sciences and Engineering Research Council of Canada and the University of Calgary. We are grateful for all of this considerable support. Almost fifty years ago the first Symposium on Lattice Theory was held in Charlottesville, U.S.A. On that occasion the principal lectures were delivered by G. Birkhoff, O. Ore and M.H. Stone. In those days the theory of ordered sets was thought to be a vigorous relative of group theory. Some twenty-five years ago the Symposium on Partially Ordered Sets and Lattice Theory was held in Monterey, U.S.A. Among the principal speakers at that meeting were R.P. Dilworth, B. Jonsson, A. Tarski and G. Birkhoff. Lattice theory had turned inward: it was concerned primarily with problems about lattices themselves. As a matter of fact the problems that were then posed have, by now, in many instances, been completely solved.

In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years.

Author: Bruno Courcelle

Publisher: Cambridge University Press

ISBN: 9780521898331

Category: Mathematics

Page: 728

View: 317

The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The authors not only provide a thorough description of the theory, but also detail its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.

graphs to be investigated in the search for cubic graphs of given order with largest girth . Our special interest in such graphs stems from certain ...

This book looks at graph theory's development and the vibrant individuals responsible for the field's growth.

Author: Arthur Benjamin

Publisher: Princeton University Press

ISBN: 9780691175638

Category: Mathematics

Page: 344

View: 430

Graph theory goes back several centuries and revolves around the study of graphs—mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics—and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducing fundamental concepts, the authors explore a diverse plethora of classic problems such as the Lights Out Puzzle, and each chapter contains math exercises for readers to savor. An eye-opening journey into the world of graphs, The Fascinating World of Graph Theory offers exciting problem-solving possibilities for mathematics and beyond.

The book is aimed mainly towards mathematicians, both researchers and doctoral students, with interest in the field of mathematical chemistry. This book is about graph energy.

Author: Xueliang Li

Publisher: Springer Science & Business Media

ISBN: 9781461442202

Category: Mathematics

Page: 268

View: 176

This book is about graph energy. The authors have included many of the important results on graph energy, such as the complete solution to the conjecture on maximal energy of unicyclic graphs, the Wagner-Heuberger’s result on the energy of trees, the energy of random graphs or the approach to energy using singular values. It contains an extensive coverage of recent results and a gradual development of topics and the inclusion of complete proofs from most of the important recent results in the area. The latter fact makes it a valuable reference for researchers looking to get into the field of graph energy, further stimulating it with occasional inclusion of open problems. The book provides a comprehensive survey of all results and common proof methods obtained in this field with an extensive reference section. The book is aimed mainly towards mathematicians, both researchers and doctoral students, with interest in the field of mathematical chemistry.

This book provides a rapid introduction to topics in graph theory typically covered in a graduate course.

Author: Hian Poh Yap

Publisher: Cambridge University Press

ISBN: 9780521339445

Category: Mathematics

Page: 230

View: 965

This book provides a rapid introduction to topics in graph theory typically covered in a graduate course. The author sets out the main recent results in several areas of current research in graph theory. Topics covered include edge-colourings, symmetries of graphs, packing of graphs, and computational complexity. Professor Yap is able to lead the reader to the forefront of research and to describe some of the open problems in the field. The choice of material presented has arisen from courses given at the National University of Singapore and each chapter contains numerous examples and exercises for the reader.

Let B be a b.s.c. graph with parts X and Y. Let C(B) denote the set of ... Constructing the Odd Order Graphs Given an input file of the b.s.c graphs ...

Abstract: Kuratowski proved that a finite graph embeds in the plane if it does not contain a subdivision of either K5 or K3, 3, called Kuratowski subgraphs.

Author: Suhkjin Hur

Publisher:

ISBN: OCLC:244294960

Category: Graphic methods

Page: 346

View: 180

Abstract: Kuratowski proved that a finite graph embeds in the plane if it does not contain a subdivision of either K5 or K3, 3, called Kuratowski subgraphs. A conjectured generalization of this result to all nonorientable surfaces says that a finite graph embeds in the nonorientable surface of genus g̃ if it does not contain g̃+1 Kuratowski subgraphs such that the union of each pair of these fails to embed in the projective plane, the union of each triple of these fails to embed in the Klein bottle if g̃>̲ 2, and the union of each triple of these fails to embed in the torus if g̃>̲ 3. We prove this conjecture for all graphs of order

A comprehensive treatment of color-induced graph colorings is presented in this book, emphasizing vertex colorings induced by edge colorings.

Author: Ping Zhang

Publisher: Springer

ISBN: 9783319203942

Category: Mathematics

Page: 118

View: 456

A comprehensive treatment of color-induced graph colorings is presented in this book, emphasizing vertex colorings induced by edge colorings. The coloring concepts described in this book depend not only on the property required of the initial edge coloring and the kind of objects serving as colors, but also on the property demanded of the vertex coloring produced. For each edge coloring introduced, background for the concept is provided, followed by a presentation of results and open questions dealing with this topic. While the edge colorings discussed can be either proper or unrestricted, the resulting vertex colorings are either proper colorings or rainbow colorings. This gives rise to a discussion of irregular colorings, strong colorings, modular colorings, edge-graceful colorings, twin edge colorings and binomial colorings. Since many of the concepts described in this book are relatively recent, the audience for this book is primarily mathematicians interested in learning some new areas of graph colorings as well as researchers and graduate students in the mathematics community, especially the graph theory community.