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Irregularity in Graphs

Author: Akbar Ali

Publisher: Springer Nature

Published: 2021-05-20

Total Pages: 109

ISBN-13: 3030679934

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Die Theorie der regularen Graphen (The Theory of Regular Graphs), written by the Danish Mathematician Julius Petersen in 1891, is often considered the first strictly theoretical paper dealing with graphs. In the 130 years since then, regular graphs have been a common and popular area of study. While regular graphs are typically considered to be graphs whose vertices all have the same degree, a more general interpretation is that of graphs possessing some common characteristic throughout their structure. During the past several decades, however, there has been some increased interest in investigating graphs possessing a property that is, in a sense, opposite to regularity. It is this topic with which this book deals, giving rise to a study of what might be called irregularity in graphs. Here, various irregularity concepts dealing with several topics in graph theory are described, such as degrees of vertices, graph labelings, weightings, colorings, graph structures, Eulerian and Hamiltonian properties, graph decompositions, and Ramsey-type problems.

Book Synopsis Irregularity in Graphs by : Akbar Ali

Download or read book Irregularity in Graphs written by Akbar Ali and published by Springer Nature. This book was released on 2021-05-20 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: Die Theorie der regularen Graphen (The Theory of Regular Graphs), written by the Danish Mathematician Julius Petersen in 1891, is often considered the first strictly theoretical paper dealing with graphs. In the 130 years since then, regular graphs have been a common and popular area of study. While regular graphs are typically considered to be graphs whose vertices all have the same degree, a more general interpretation is that of graphs possessing some common characteristic throughout their structure. During the past several decades, however, there has been some increased interest in investigating graphs possessing a property that is, in a sense, opposite to regularity. It is this topic with which this book deals, giving rise to a study of what might be called irregularity in graphs. Here, various irregularity concepts dealing with several topics in graph theory are described, such as degrees of vertices, graph labelings, weightings, colorings, graph structures, Eulerian and Hamiltonian properties, graph decompositions, and Ramsey-type problems.

Even Modular Edge Irregularity Strength of Graphs

Author: K.Muthugurupackiam

Publisher: Infinite Study

Published:

Total Pages: 8

ISBN-13:

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A new graph characteristic, even modular edge irregularity strength of graphs is introduced. Estimation on this parameter is obtained and the precise values of this parameter are obtained for some families of graphs.

Book Synopsis Even Modular Edge Irregularity Strength of Graphs by : K.Muthugurupackiam

Download or read book Even Modular Edge Irregularity Strength of Graphs written by K.Muthugurupackiam and published by Infinite Study. This book was released on with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new graph characteristic, even modular edge irregularity strength of graphs is introduced. Estimation on this parameter is obtained and the precise values of this parameter are obtained for some families of graphs.

Spectral Radius of Graphs

Author: Dragan Stevanovic

Publisher: Academic Press

Published: 2014-10-13

Total Pages: 167

ISBN-13: 0128020970

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Spectral Radius of Graphs provides a thorough overview of important results on the spectral radius of adjacency matrix of graphs that have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author. The primer begins with a brief classical review, in order to provide the reader with a foundation for the subsequent chapters. Topics covered include spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem. From this introduction, the book delves deeper into the properties of the principal eigenvector; a critical subject as many of the results on the spectral radius of graphs rely on the properties of the principal eigenvector for their proofs. A following chapter surveys spectral radius of special graphs, covering multipartite graphs, non-regular graphs, planar graphs, threshold graphs, and others. Finally, the work explores results on the structure of graphs having extreme spectral radius in classes of graphs defined by fixing the value of a particular, integer-valued graph invariant, such as: the diameter, the radius, the domination number, the matching number, the clique number, the independence number, the chromatic number or the sequence of vertex degrees. Throughout, the text includes the valuable addition of proofs to accompany the majority of presented results. This enables the reader to learn tricks of the trade and easily see if some of the techniques apply to a current research problem, without having to spend time on searching for the original articles. The book also contains a handful of open problems on the topic that might provide initiative for the reader's research. Dedicated coverage to one of the most prominent graph eigenvalues Proofs and open problems included for further study Overview of classical topics such as spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem

Book Synopsis Spectral Radius of Graphs by : Dragan Stevanovic

Download or read book Spectral Radius of Graphs written by Dragan Stevanovic and published by Academic Press. This book was released on 2014-10-13 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral Radius of Graphs provides a thorough overview of important results on the spectral radius of adjacency matrix of graphs that have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author. The primer begins with a brief classical review, in order to provide the reader with a foundation for the subsequent chapters. Topics covered include spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem. From this introduction, the book delves deeper into the properties of the principal eigenvector; a critical subject as many of the results on the spectral radius of graphs rely on the properties of the principal eigenvector for their proofs. A following chapter surveys spectral radius of special graphs, covering multipartite graphs, non-regular graphs, planar graphs, threshold graphs, and others. Finally, the work explores results on the structure of graphs having extreme spectral radius in classes of graphs defined by fixing the value of a particular, integer-valued graph invariant, such as: the diameter, the radius, the domination number, the matching number, the clique number, the independence number, the chromatic number or the sequence of vertex degrees. Throughout, the text includes the valuable addition of proofs to accompany the majority of presented results. This enables the reader to learn tricks of the trade and easily see if some of the techniques apply to a current research problem, without having to spend time on searching for the original articles. The book also contains a handful of open problems on the topic that might provide initiative for the reader's research. Dedicated coverage to one of the most prominent graph eigenvalues Proofs and open problems included for further study Overview of classical topics such as spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem

A Study of Regular and Irregular Neutrosophic Graphs with Real Life Applications

Author: Liangsong Huang

Publisher: Infinite Study

Published:

Total Pages: 20

ISBN-13:

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Fuzzy graph theory is a useful and well-known tool to model and solve many real-life optimization problems. Since real-life problems are often uncertain due to inconsistent and indeterminate information, it is very hard for an expert to model those problems using a fuzzy graph. A neutrosophic graph can deal with the uncertainty associated with the inconsistent and indeterminate information of any real-world problem, where fuzzy graphs may fail to reveal satisfactory results.

Book Synopsis A Study of Regular and Irregular Neutrosophic Graphs with Real Life Applications by : Liangsong Huang

Download or read book A Study of Regular and Irregular Neutrosophic Graphs with Real Life Applications written by Liangsong Huang and published by Infinite Study. This book was released on with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fuzzy graph theory is a useful and well-known tool to model and solve many real-life optimization problems. Since real-life problems are often uncertain due to inconsistent and indeterminate information, it is very hard for an expert to model those problems using a fuzzy graph. A neutrosophic graph can deal with the uncertainty associated with the inconsistent and indeterminate information of any real-world problem, where fuzzy graphs may fail to reveal satisfactory results.

Color-Induced Graph Colorings

Author: Ping Zhang

Publisher: Springer

Published: 2015-08-10

Total Pages: 118

ISBN-13: 3319203940

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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.

Book Synopsis Color-Induced Graph Colorings by : Ping Zhang

Download or read book Color-Induced Graph Colorings written by Ping Zhang and published by Springer. This book was released on 2015-08-10 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Efficient Execution of Irregular Dataflow Graphs

Author: Nimish Shah

Publisher: Springer Nature

Published: 2023-08-14

Total Pages: 155

ISBN-13: 3031331362

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This book focuses on the acceleration of emerging irregular sparse workloads, posed by novel artificial intelligent (AI) models and sparse linear algebra. Specifically, the book outlines several co-optimized hardware-software solutions for a highly promising class of emerging sparse AI models called Probabilistic Circuit (PC) and a similar sparse matrix workload for triangular linear systems (SpTRSV). The authors describe optimizations for the entire stack, targeting applications, compilation, hardware architecture and silicon implementation, resulting in orders of magnitude higher performance and energy-efficiency compared to the existing state-of-the-art solutions. Thus, this book provides important building blocks for the upcoming generation of edge AI platforms.

Book Synopsis Efficient Execution of Irregular Dataflow Graphs by : Nimish Shah

Download or read book Efficient Execution of Irregular Dataflow Graphs written by Nimish Shah and published by Springer Nature. This book was released on 2023-08-14 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the acceleration of emerging irregular sparse workloads, posed by novel artificial intelligent (AI) models and sparse linear algebra. Specifically, the book outlines several co-optimized hardware-software solutions for a highly promising class of emerging sparse AI models called Probabilistic Circuit (PC) and a similar sparse matrix workload for triangular linear systems (SpTRSV). The authors describe optimizations for the entire stack, targeting applications, compilation, hardware architecture and silicon implementation, resulting in orders of magnitude higher performance and energy-efficiency compared to the existing state-of-the-art solutions. Thus, this book provides important building blocks for the upcoming generation of edge AI platforms.

MATHEMATICAL COMBINATORICS (INTERNATIONAL BOOK SERIES)

Author: Linfan MAO

Publisher: Infinite Study

Published:

Total Pages: 135

ISBN-13:

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The mathematical combinatorics is a subject that applying combinatorial notion to all mathematics and all sciences for understanding the reality of things in the universe, motivated by CC Conjecture of Dr.Linfan MAO on mathematical sciences. TheMathematical Combinatorics (International Book Series) is a fully refereed international book series with an ISBN number on each issue, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly, which publishes original research papers and survey articles in all aspects of mathematical combinatorics, Smarandachemulti-spaces, Smarandache geometries, non-Euclidean geometry, topology and their applications to other sciences.

Book Synopsis MATHEMATICAL COMBINATORICS (INTERNATIONAL BOOK SERIES) by : Linfan MAO

Download or read book MATHEMATICAL COMBINATORICS (INTERNATIONAL BOOK SERIES) written by Linfan MAO and published by Infinite Study. This book was released on with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical combinatorics is a subject that applying combinatorial notion to all mathematics and all sciences for understanding the reality of things in the universe, motivated by CC Conjecture of Dr.Linfan MAO on mathematical sciences. TheMathematical Combinatorics (International Book Series) is a fully refereed international book series with an ISBN number on each issue, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly, which publishes original research papers and survey articles in all aspects of mathematical combinatorics, Smarandachemulti-spaces, Smarandache geometries, non-Euclidean geometry, topology and their applications to other sciences.

Data Science and Security

Author: Dharm Singh Jat

Publisher: Springer Nature

Published: 2020-07-31

Total Pages: 321

ISBN-13: 9811553092

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This book presents best selected papers presented at the International Conference on Data Science for Computational Security (IDSCS 2020), organized by the Department of Data Science, CHRIST (Deemed to be University), Pune Lavasa Campus, India, during 13–14 March 2020. The proceeding will be targeting the current research works in the areas of data science, data security, data analytics, artificial intelligence, machine learning, computer vision, algorithms design, computer networking, data mining, big data, text mining, knowledge representation, soft computing and cloud computing.

Book Synopsis Data Science and Security by : Dharm Singh Jat

Download or read book Data Science and Security written by Dharm Singh Jat and published by Springer Nature. This book was released on 2020-07-31 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents best selected papers presented at the International Conference on Data Science for Computational Security (IDSCS 2020), organized by the Department of Data Science, CHRIST (Deemed to be University), Pune Lavasa Campus, India, during 13–14 March 2020. The proceeding will be targeting the current research works in the areas of data science, data security, data analytics, artificial intelligence, machine learning, computer vision, algorithms design, computer networking, data mining, big data, text mining, knowledge representation, soft computing and cloud computing.

The Fascinating World of Graph Theory

Author: Arthur Benjamin

Publisher: Princeton University Press

Published: 2017-06-06

Total Pages: 338

ISBN-13: 0691175632

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The history, formulas, and most famous puzzles of graph theory 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.

Book Synopsis The Fascinating World of Graph Theory by : Arthur Benjamin

Download or read book The Fascinating World of Graph Theory written by Arthur Benjamin and published by Princeton University Press. This book was released on 2017-06-06 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The history, formulas, and most famous puzzles of graph theory 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.

Fuzzy Graph Theory

Author: Sunil Mathew

Publisher: Springer

Published: 2017-12-30

Total Pages: 320

ISBN-13: 3319714074

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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.

Book Synopsis Fuzzy Graph Theory by : Sunil Mathew

Download or read book Fuzzy Graph Theory written by Sunil Mathew and published by Springer. This book was released on 2017-12-30 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.