Graph Theory

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Ping Zhang - One of the best experts on this subject based on the ideXlab platform.

  • The Fascinating World of Graph Theory
    2017
    Co-Authors: Ping Zhang, Gary Chartrand, Arthur Benjamin
    Abstract:

    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. This book explores the questions and puzzles that have been studied, and often solved, through Graph Theory. It looks at Graph Theory's development and the vibrant individuals responsible for the field's growth. Introducing fundamental concepts, the book explores 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 book offers exciting problem-solving possibilities for mathematics and beyond.

  • The Fascinating World of Graph Theory - Graph Theory: A Look Back—The Road Ahead
    The Fascinating World of Graph Theory, 2017
    Co-Authors: Arthur T. Benjamin, Gary Chartrand, Ping Zhang
    Abstract:

    This book concludes with an epilogue, which traces the evolution of Graph Theory, from the conceptualization of the Königsberg Bridge Problem and its generalization by Leonhard Euler, whose solution led to the subject of Eulerian Graphs, to the various efforts to solve the Four Color Problem. It considers elements of Graph Theory found in games and puzzles of the past, and the famous mathematicians involved including Sir William Rowan Hamilton and William Tutte. It also discusses the remarkable increase since the 1960s in the number of mathematicians worldwide devoted to Graph Theory, along with research journals, books, and monoGraphs that have Graph Theory as a subject. Finally, it looks at the growth in applications of Graph Theory dealing with communication and social networks and the Internet in the digital age and the age of technology.

  • The Fascinating World of Graph Theory
    2015
    Co-Authors: Arthur Benjamin, Gary Chartrand, Ping Zhang
    Abstract:

    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\u27s development and the vibrant individuals responsible for the field\u27s 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.https://scholarship.claremont.edu/hmc_facbooks/1037/thumbnail.jp

  • Handbook of Graph Theory, Second Edition - Handbook of Graph Theory, Second Edition
    2013
    Co-Authors: Jonathan L Gross, Jay Yellen, Ping Zhang
    Abstract:

    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 editionover 400 pages longer than its predecessorincorporates 14 new sections. Each chapter includes lists of essential definitions and facts, accompanied by examples, tables, remarks, and, in some cases, conjectures and open problems. A biblioGraphy at the end of each chapter provides an extensive guide to the research literature and pointers to monoGraphs. In addition, a glossary is included in each chapter as well as at the end of each section. This edition also contains notes regarding terminology and notation. With 34 new contributors, this handbook is the most comprehensive single-source guide to Graph Theory. It emphasizes quick accessibility to topics for non-experts and enables easy cross-referencing among chapters.

  • handbook of Graph Theory second edition
    2013
    Co-Authors: Jonathan L Gross, Jay Yellen, Ping Zhang
    Abstract:

    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 editionover 400 pages longer than its predecessorincorporates 14 new sections. Each chapter includes lists of essential definitions and facts, accompanied by examples, tables, remarks, and, in some cases, conjectures and open problems. A biblioGraphy at the end of each chapter provides an extensive guide to the research literature and pointers to monoGraphs. In addition, a glossary is included in each chapter as well as at the end of each section. This edition also contains notes regarding terminology and notation. With 34 new contributors, this handbook is the most comprehensive single-source guide to Graph Theory. It emphasizes quick accessibility to topics for non-experts and enables easy cross-referencing among chapters.

Yongtang Shi - One of the best experts on this subject based on the ideXlab platform.

  • Quantitative Graph Theory: A new branch of Graph Theory and in network science
    arXiv: Social and Information Networks, 2017
    Co-Authors: Matthias Dehmer, Frank Emmert-streib, Yongtang Shi
    Abstract:

    In this paper, we describe {\sc quantitative Graph Theory} and argue it is a new Graph-theoretical branch in network science, however, with significant different features compared to classical Graph Theory. The main goal of quantitative Graph Theory is the structural quantification of information contained in complex networks by employing a {\it measurement approach} based on numerical invariants and comparisons. Furthermore, the methods as well as the networks do not need to be deterministic but can be statistic. As such this complements the field of classical Graph Theory, which is descriptive and deterministic in nature. We provide examples of how quantitative Graph Theory can be used for novel applications in the context of the overarching concept network science.

  • Quantitative Graph Theory
    Information Sciences, 2017
    Co-Authors: Matthias Dehmer, Frank Emmert-streib, Yongtang Shi
    Abstract:

    In this paper, we describe some highlights of the new branch quantitative Graph Theory and explain its significant different features compared to classical Graph Theory. The main goal of quantitative Graph Theory is the structural quantification of information contained in complex networks by employing a measurement approach based on numerical invariants and comparisons. Furthermore, the methods as well as the networks do not need to be deterministic but can be statistic. As such this complements the field of classical Graph Theory, which is descriptive and deterministic in nature. We provide examples of how quantitative Graph Theory can be used for novel applications in the context of the overarching concept network science.

Matthias Dehmer - One of the best experts on this subject based on the ideXlab platform.

  • Quantitative Graph Theory: A new branch of Graph Theory and in network science
    arXiv: Social and Information Networks, 2017
    Co-Authors: Matthias Dehmer, Frank Emmert-streib, Yongtang Shi
    Abstract:

    In this paper, we describe {\sc quantitative Graph Theory} and argue it is a new Graph-theoretical branch in network science, however, with significant different features compared to classical Graph Theory. The main goal of quantitative Graph Theory is the structural quantification of information contained in complex networks by employing a {\it measurement approach} based on numerical invariants and comparisons. Furthermore, the methods as well as the networks do not need to be deterministic but can be statistic. As such this complements the field of classical Graph Theory, which is descriptive and deterministic in nature. We provide examples of how quantitative Graph Theory can be used for novel applications in the context of the overarching concept network science.

  • Quantitative Graph Theory
    Information Sciences, 2017
    Co-Authors: Matthias Dehmer, Frank Emmert-streib, Yongtang Shi
    Abstract:

    In this paper, we describe some highlights of the new branch quantitative Graph Theory and explain its significant different features compared to classical Graph Theory. The main goal of quantitative Graph Theory is the structural quantification of information contained in complex networks by employing a measurement approach based on numerical invariants and comparisons. Furthermore, the methods as well as the networks do not need to be deterministic but can be statistic. As such this complements the field of classical Graph Theory, which is descriptive and deterministic in nature. We provide examples of how quantitative Graph Theory can be used for novel applications in the context of the overarching concept network science.

  • What Is Quantitative Graph Theory?
    Discrete Mathematics and Its Applications, 2014
    Co-Authors: Matthias Dehmer, Frank Emmert-streib, Veronika Kraus, Stefan Pickl
    Abstract:

    The first book devoted exclusively to quantitative Graph Theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing Graphs quantitatively. Incorporating interdisciplinary knowledge from Graph Theory, information Theory, measurement Theory, and statistical techniques, this book covers a wide range of quantitative-Graph theoretical concepts and methods, including those pertaining to real and random Graphs such as: Comparative approaches (Graph similarity or distance) Graph measures to characterize Graphs quantitatively Applications of Graph measures in social network analysis and other disciplines Metrical properties of Graphs and measures Mathematical properties of quantitative methods or measures in Graph Theory Network complexity measures and other topological indices Quantitative approaches to Graphs using machine learning (e.g., clustering) Graph measures and statistics Information-theoretic methods to analyze Graphs quantitatively (e.g., entropy) Through its broad coverage, Quantitative Graph Theory: Mathematical Foundations and Applications fills a gap in the contemporary literature of discrete and applied mathematics, computer science, systems biology, and related disciplines. It is intended for researchers as well as graduate and advanced undergraduate students in the fields of mathematics, computer science, mathematical chemistry, cheminformatics, physics, bioinformatics, and systems biology.Postprint (published version

Wang Gao-cai - One of the best experts on this subject based on the ideXlab platform.

Frank Emmert-streib - One of the best experts on this subject based on the ideXlab platform.

  • Quantitative Graph Theory: A new branch of Graph Theory and in network science
    arXiv: Social and Information Networks, 2017
    Co-Authors: Matthias Dehmer, Frank Emmert-streib, Yongtang Shi
    Abstract:

    In this paper, we describe {\sc quantitative Graph Theory} and argue it is a new Graph-theoretical branch in network science, however, with significant different features compared to classical Graph Theory. The main goal of quantitative Graph Theory is the structural quantification of information contained in complex networks by employing a {\it measurement approach} based on numerical invariants and comparisons. Furthermore, the methods as well as the networks do not need to be deterministic but can be statistic. As such this complements the field of classical Graph Theory, which is descriptive and deterministic in nature. We provide examples of how quantitative Graph Theory can be used for novel applications in the context of the overarching concept network science.

  • Quantitative Graph Theory
    Information Sciences, 2017
    Co-Authors: Matthias Dehmer, Frank Emmert-streib, Yongtang Shi
    Abstract:

    In this paper, we describe some highlights of the new branch quantitative Graph Theory and explain its significant different features compared to classical Graph Theory. The main goal of quantitative Graph Theory is the structural quantification of information contained in complex networks by employing a measurement approach based on numerical invariants and comparisons. Furthermore, the methods as well as the networks do not need to be deterministic but can be statistic. As such this complements the field of classical Graph Theory, which is descriptive and deterministic in nature. We provide examples of how quantitative Graph Theory can be used for novel applications in the context of the overarching concept network science.

  • What Is Quantitative Graph Theory?
    Discrete Mathematics and Its Applications, 2014
    Co-Authors: Matthias Dehmer, Frank Emmert-streib, Veronika Kraus, Stefan Pickl
    Abstract:

    The first book devoted exclusively to quantitative Graph Theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing Graphs quantitatively. Incorporating interdisciplinary knowledge from Graph Theory, information Theory, measurement Theory, and statistical techniques, this book covers a wide range of quantitative-Graph theoretical concepts and methods, including those pertaining to real and random Graphs such as: Comparative approaches (Graph similarity or distance) Graph measures to characterize Graphs quantitatively Applications of Graph measures in social network analysis and other disciplines Metrical properties of Graphs and measures Mathematical properties of quantitative methods or measures in Graph Theory Network complexity measures and other topological indices Quantitative approaches to Graphs using machine learning (e.g., clustering) Graph measures and statistics Information-theoretic methods to analyze Graphs quantitatively (e.g., entropy) Through its broad coverage, Quantitative Graph Theory: Mathematical Foundations and Applications fills a gap in the contemporary literature of discrete and applied mathematics, computer science, systems biology, and related disciplines. It is intended for researchers as well as graduate and advanced undergraduate students in the fields of mathematics, computer science, mathematical chemistry, cheminformatics, physics, bioinformatics, and systems biology.Postprint (published version

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