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Zero Forcing Sets and Bipartite Circulants

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Author :
Release : 2012
Genre :
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Zero Forcing Sets and Bipartite Circulants by :

Download or read book Zero Forcing Sets and Bipartite Circulants written by . This book was released on 2012. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we introduce a class of regular bipartite graphs whose biadjacency matrices are circulant matrices -- a generalization of circulant graphs which happen to be bipartite -- and we describe some properties possessed by these graphs. We describe sufficient conditions for two of these graphs to be isomorphic and prove necessary conditions in some cases. We also compute upper and lower bounds for the zero forcing number of such a graph based only on the parameters that describe its biadjacency matrix. The main results of this thesis characterize the bipartite circulant graphs that achieve equality in the lower bound and compute their minimum ranks.

Inverse Problems and Zero Forcing for Graphs

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Author :
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.

Graph Representation Learning

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Author :
Release : 2022-06-01
Genre : Computers
Kind : eBook
Book Rating : 886/5 ( reviews)

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Book Synopsis Graph Representation Learning by : William L. William L. Hamilton

Download or read book Graph Representation Learning written by William L. William L. Hamilton. This book was released on 2022-06-01. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Pearls in Graph Theory

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Author :
Release : 2013-04-15
Genre : Mathematics
Kind : eBook
Book Rating : 525/5 ( reviews)

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Book Synopsis Pearls in Graph Theory by : Nora Hartsfield

Download or read book Pearls in Graph Theory written by Nora Hartsfield. This book was released on 2013-04-15. Available in PDF, EPUB and Kindle. Book excerpt: Stimulating and accessible, this undergraduate-level text covers basic graph theory, colorings of graphs, circuits and cycles, labeling graphs, drawings of graphs, measurements of closeness to planarity, graphs on surfaces, and applications and algorithms. 1994 edition.

Spectra of Graphs

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Author :
Release : 2011-12-17
Genre : Mathematics
Kind : eBook
Book Rating : 395/5 ( reviews)

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Book Synopsis Spectra of Graphs by : Andries E. Brouwer

Download or read book Spectra of Graphs written by Andries E. Brouwer. This book was released on 2011-12-17. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics. Exercises at the end of each chapter provide practice and vary from easy yet interesting applications of the treated theory, to little excursions into related topics. Tables, references at the end of the book, an author and subject index enrich the text. Spectra of Graphs is written for researchers, teachers and graduate students interested in graph spectra. The reader is assumed to be familiar with basic linear algebra and eigenvalues, although some more advanced topics in linear algebra, like the Perron-Frobenius theorem and eigenvalue interlacing are included.

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