Generalized Connectivity Of Graphs
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Author | : Xueliang Li |
Publisher | : Springer |
Total Pages | : 148 |
Release | : 2016-06-30 |
Genre | : Mathematics |
ISBN | : 3319338285 |
Noteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations with the Steiner tree packing problem and generalizations of connectivity. This book enables graduate students to understand and master a segment of graph theory and combinatorial optimization. Researchers in graph theory, combinatorics, combinatorial optimization, probability, computer science, discrete algorithms, complexity analysis, network design, and the information transferring models will find this book useful in their studies.
Author | : Ortrud R. Oellermann |
Publisher | : |
Total Pages | : 280 |
Release | : 1986 |
Genre | : Graph theory |
ISBN | : |
Author | : |
Publisher | : |
Total Pages | : 576 |
Release | : 1979 |
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Author | : Sunil Mathew |
Publisher | : Springer |
Total Pages | : 331 |
Release | : 2017-12-30 |
Genre | : Technology & Engineering |
ISBN | : 3319714074 |
This book provides a timely overview of fuzzy graph theory, laying the foundation for future applications in a broad range of areas. It introduces readers to fundamental theories, such as Craine’s work on fuzzy interval graphs, fuzzy analogs of Marczewski’s theorem, and the Gilmore and Hoffman characterization. It also introduces them to the Fulkerson and Gross characterization and Menger’s theorem, the applications of which will be discussed in a forthcoming book by the same authors. This book also discusses in detail important concepts such as connectivity, distance and saturation in fuzzy graphs. Thanks to the good balance between the basics of fuzzy graph theory and new findings obtained by the authors, the book offers an excellent reference guide for advanced undergraduate and graduate students in mathematics, engineering and computer science, and an inspiring read for all researchers interested in new developments in fuzzy logic and applied mathematics.
Author | : Lowell W. Beineke |
Publisher | : Cambridge University Press |
Total Pages | : 346 |
Release | : 2012-11-08 |
Genre | : Mathematics |
ISBN | : 1107244307 |
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.
Author | : Alan Frieze |
Publisher | : Cambridge University Press |
Total Pages | : 483 |
Release | : 2016 |
Genre | : Mathematics |
ISBN | : 1107118506 |
The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.
Author | : William L. William L. Hamilton |
Publisher | : Springer Nature |
Total Pages | : 141 |
Release | : 2022-06-01 |
Genre | : Computers |
ISBN | : 3031015886 |
Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.
Author | : Remco van der Hofstad |
Publisher | : Cambridge University Press |
Total Pages | : 341 |
Release | : 2017 |
Genre | : Computers |
ISBN | : 110717287X |
This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.
Author | : Lucas C. Van der Merwe |
Publisher | : |
Total Pages | : 46 |
Release | : 1997 |
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Author | : W. T. Tutte |
Publisher | : |
Total Pages | : 164 |
Release | : 1966 |
Genre | : Mathematics |
ISBN | : |