Fundamentals of Graph Theory

Fundamentals of Graph Theory
Author: Allan Bickle
Publisher: American Mathematical Soc.
Total Pages: 336
Release: 2020-03-10
Genre: Education
ISBN: 1470453428

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Graph theory is a fascinating and inviting branch of mathematics. Many problems are easy to state and have natural visual representations, inviting exploration by new students and professional mathematicians. The goal of this textbook is to present the fundamentals of graph theory to a wide range of readers. The book contains many significant recent results in graph theory, presented using up-to-date notation. The author included the shortest, most elegant, most intuitive proofs for modern and classic results while frequently presenting them in new ways. Major topics are introduced with practical applications that motivate their development, and which are illustrated with examples that show how to apply major theorems in practice. This includes the process of finding a brute force solution (case-checking) when an elegant solution is not apparent. With over 1200 exercises, internet resources (e.g., the OEIS for counting problems), helpful appendices, and a detailed guide to different course outlines, this book provides a versatile and convenient tool for the needs of instructors at a large variety of institutions.

Fundamentals of Graph Theory

Fundamentals of Graph Theory
Author: Allan Bickle
Publisher:
Total Pages: 354
Release:
Genre: Graph theory
ISBN: 9781470455491

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Graph theory is a fascinating and inviting branch of mathematics. Many problems are easy to state and have natural visual representations, inviting exploration by new students and professional mathematicians. The goal of this textbook is to present the fundamentals of graph theory to a wide range of readers. The book contains many significant recent results in graph theory, presented using up-to-date notation. The author included the shortest, most elegant, most intuitive proofs for modern and classic results while frequently presenting them in new ways. Major topics are introduced with practi.

Chemical Graph Theory

Chemical Graph Theory
Author: D Bonchev
Publisher: Routledge
Total Pages: 310
Release: 2018-05-11
Genre: Science
ISBN: 1351461591

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This volume presents the fundamentals of graph theory and then goes on to discuss specific chemical applications. Chapter 1 provides a historical setting for the current upsurge of interest in chemical graph theory. Chapter 2 gives a full background of the basic ideas and mathematical formalism of graph theory and includes such chemically relevant notions as connectedness, graph matrix representations, metric properties, symmetry and operations on graphs. This is followed by a discussion on chemical nomenclature and the trends in its rationalization by using graph theory, which has important implications for the storage and retrieval of chemical information. This volume also contains a detailed discussion of the relevance of graph-theoretical polynomials; it describes methodologies for the enumeration of isomers, incorporating the classical Polya method, as well as more recent approaches.

Fundamentals of Algebraic Graph Transformation

Fundamentals of Algebraic Graph Transformation
Author: Hartmut Ehrig
Publisher: Springer Science & Business Media
Total Pages: 383
Release: 2006-05-01
Genre: Computers
ISBN: 3540311882

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This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. It contains an introduction to classical graphs. Basic and advanced results are first shown for an abstract form of replacement systems and are then instantiated to several forms of graph and Petri net transformation systems. The book develops typed attributed graph transformation and contains a practical case study.

Chromatic Graph Theory

Chromatic Graph Theory
Author: Gary Chartrand
Publisher: CRC Press
Total Pages: 503
Release: 2019-11-28
Genre: Mathematics
ISBN: 0429798288

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With Chromatic Graph Theory, Second Edition, the authors present various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. Readers will see that the authors accomplished the primary goal of this textbook, which is to introduce graph theory with a coloring theme and to look at graph colorings in various ways. The textbook also covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings. Features of the Second Edition: The book can be used for a first course in graph theory as well as a graduate course The primary topic in the book is graph coloring The book begins with an introduction to graph theory so assumes no previous course The authors are the most widely-published team on graph theory Many new examples and exercises enhance the new edition

Fundamentals of Domination in Graphs

Fundamentals of Domination in Graphs
Author: Teresa W. Haynes
Publisher: CRC Press
Total Pages: 465
Release: 2013-12-16
Genre: Mathematics
ISBN: 1482246589

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"Provides the first comprehensive treatment of theoretical, algorithmic, and application aspects of domination in graphs-discussing fundamental results and major research accomplishments in an easy-to-understand style. Includes chapters on domination algorithms and NP-completeness as well as frameworks for domination."

Introduction to Graph Theory

Introduction to Graph Theory
Author: Richard J. Trudeau
Publisher: Courier Corporation
Total Pages: 224
Release: 2013-04-15
Genre: Mathematics
ISBN: 0486318664

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Aimed at "the mathematically traumatized," this text offers nontechnical coverage of graph theory, with exercises. Discusses planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. 1976 edition.

Fundamentals of Graph Theory

Fundamentals of Graph Theory
Author: Aleksandr Aleksandrovich Zykov
Publisher:
Total Pages: 392
Release: 1990
Genre: Mathematics
ISBN:

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Introduction to Graph Theory

Introduction to Graph Theory
Author: Koh Khee Meng
Publisher: World Scientific Publishing Company
Total Pages: 244
Release: 2007-03-15
Genre: Mathematics
ISBN: 9813101636

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Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory and, in particular, as a resource book for junior college students and teachers reading and teaching the subject at H3 Level in the new Singapore mathematics curriculum for junior college. The book builds on the verity that graph theory at this level is a subject that lends itself well to the development of mathematical reasoning and proof.

Fundamentals of Brain Network Analysis

Fundamentals of Brain Network Analysis
Author: Alex Fornito
Publisher: Academic Press
Total Pages: 494
Release: 2016-03-04
Genre: Medical
ISBN: 0124081185

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Fundamentals of Brain Network Analysis is a comprehensive and accessible introduction to methods for unraveling the extraordinary complexity of neuronal connectivity. From the perspective of graph theory and network science, this book introduces, motivates and explains techniques for modeling brain networks as graphs of nodes connected by edges, and covers a diverse array of measures for quantifying their topological and spatial organization. It builds intuition for key concepts and methods by illustrating how they can be practically applied in diverse areas of neuroscience, ranging from the analysis of synaptic networks in the nematode worm to the characterization of large-scale human brain networks constructed with magnetic resonance imaging. This text is ideally suited to neuroscientists wanting to develop expertise in the rapidly developing field of neural connectomics, and to physical and computational scientists wanting to understand how these quantitative methods can be used to understand brain organization. Extensively illustrated throughout by graphical representations of key mathematical concepts and their practical applications to analyses of nervous systems Comprehensively covers graph theoretical analyses of structural and functional brain networks, from microscopic to macroscopic scales, using examples based on a wide variety of experimental methods in neuroscience Designed to inform and empower scientists at all levels of experience, and from any specialist background, wanting to use modern methods of network science to understand the organization of the brain