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Inverse Problems and Zero Forcing for Graphs

2022-07-21 Mathematics
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Release : 2022-07-21
Genre : Mathematics
Kind : eBook
Book Rating : 554/5 ( reviews)

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Book Synopsis Inverse Problems and Zero Forcing for Graphs by : Leslie Hogben

Download or read book Inverse Problems and Zero Forcing for Graphs written by Leslie Hogben. This book was released on 2022-07-21. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the inverse eigenvalue problem for graphs (IEP-$G$) and the related area of zero forcing, propagation, and throttling. The IEP-$G$ grew from the intersection of linear algebra and combinatorics and has given rise to both a rich set of deep problems in that area as well as a breadth of “ancillary” problems in related areas. The IEP-$G$ asks a fundamental mathematical question expressed in terms of linear algebra and graph theory, but the significance of such questions goes beyond these two areas, as particular instances of the IEP-$G$ also appear as major research problems in other fields of mathematics, sciences and engineering. One approach to the IEP-$G$ is through rank minimization, a relevant problem in itself and with a large number of applications. During the past 10 years, important developments on the rank minimization problem, particularly in relation to zero forcing, have led to significant advances in the IEP-$G$. The monograph serves as an entry point and valuable resource that will stimulate future developments in this active and mathematically diverse research area.

Research Trends in Graph Theory and Applications

2021-09-06 Mathematics
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Release : 2021-09-06
Genre : Mathematics
Kind : eBook
Book Rating : 831/5 ( reviews)

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Book Synopsis Research Trends in Graph Theory and Applications by : Daniela Ferrero

Download or read book Research Trends in Graph Theory and Applications written by Daniela Ferrero. This book was released on 2021-09-06. Available in PDF, EPUB and Kindle. Book excerpt: The Workshop for Women in Graph Theory and Applications was held at the Institute for Mathematics and Its Applications (University of Minnesota, Minneapolis) on August 19-23, 2019. During this five-day workshop, 42 participants performed collaborative research, in six teams, each focused on open problems in different areas of graph theory and its applications. The research work of each team was led by two experts in the corresponding area, who prior to the workshop, carefully selected relevant and meaningful open problems that would yield high-quality research and results of strong impact. As a result, all six teams have made significant contributions to several open problems in their respective areas. The workshop led to the creation of the Women in Graph Theory and Applications Research Collaboration Network, which provided the framework to continue collaborating and to produce this volume. This book contains six chapters, each of them on one of the different areas of research at the Workshop for Women in Graph Theory and Applications, and written by participants of each team.

The Minimum Rank, Inverse Inertia, and Inverse Eigenvalue Problems for Graphs

2010
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Release : 2010
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Book Synopsis The Minimum Rank, Inverse Inertia, and Inverse Eigenvalue Problems for Graphs by : Mark Condie Kempton

Download or read book The Minimum Rank, Inverse Inertia, and Inverse Eigenvalue Problems for Graphs written by Mark Condie Kempton. This book was released on 2010. Available in PDF, EPUB and Kindle. Book excerpt: For a graph G we define S(G) to be the set of all real symmetric n by n matrices whose off-diagonal zero/nonzero pattern is described by G. We show how to compute the minimum rank of all matrices in S(G) for a class of graphs called outerplanar graphs. In addition, we obtain results on the possible eigenvalues and possible inertias of matrices in S(G) for certain classes of graph G. We also obtain results concerning the relationship between two graph parameters, the zero forcing number and the path cover number, related to the minimum rank problem.

50 years of Combinatorics, Graph Theory, and Computing

2019-11-15 Mathematics
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Release : 2019-11-15
Genre : Mathematics
Kind : eBook
Book Rating : 83X/5 ( reviews)

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Book Synopsis 50 years of Combinatorics, Graph Theory, and Computing by : Fan Chung

Download or read book 50 years of Combinatorics, Graph Theory, and Computing written by Fan Chung. This book was released on 2019-11-15. Available in PDF, EPUB and Kindle. Book excerpt: 50 Years of Combinatorics, Graph Theory, and Computing advances research in discrete mathematics by providing current research surveys, each written by experts in their subjects. The book also celebrates outstanding mathematics from 50 years at the Southeastern International Conference on Combinatorics, Graph Theory & Computing (SEICCGTC). The conference is noted for the dissemination and stimulation of research, while fostering collaborations among mathematical scientists at all stages of their careers. The authors of the chapters highlight open questions. The sections of the book include: Combinatorics; Graph Theory; Combinatorial Matrix Theory; Designs, Geometry, Packing and Covering. Readers will discover the breadth and depth of the presentations at the SEICCGTC, as well as current research in combinatorics, graph theory and computer science. Features: Commemorates 50 years of the Southeastern International Conference on Combinatorics, Graph Theory & Computing with research surveys Surveys highlight open questions to inspire further research Chapters are written by experts in their fields Extensive bibliographies are provided at the end of each chapter

Zero Forcing in Graphs and Digraphs

2018 Graph theory
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Release : 2018
Genre : Graph theory
Kind : eBook
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Book Synopsis Zero Forcing in Graphs and Digraphs by : Esther Dawn Conrad

Download or read book Zero Forcing in Graphs and Digraphs written by Esther Dawn Conrad. This book was released on 2018. Available in PDF, EPUB and Kindle. Book excerpt:

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