Download or read book Spectral Generalizations of Line Graphs written by Dragoš Cvetkovic and published by Cambridge University Press. This book was released on 2004-07-22 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction -- Forbidden subgraphs -- Root systems -- Regular graphs -- Star complements -- The Maximal exceptional graphs -- Miscellaneous results.
Download or read book Line Graphs and Line Digraphs written by Lowell W. Beineke and published by Springer Nature. This book was released on 2021-10-29 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present era dominated by computers, graph theory has come into its own as an area of mathematics, prominent for both its theory and its applications. One of the richest and most studied types of graph structures is that of the line graph, where the focus is more on the edges of a graph than on the vertices. A subject worthy of exploration in itself, line graphs are closely connected to other areas of mathematics and computer science. This book is unique in its extensive coverage of many areas of graph theory applicable to line graphs. The book has three parts. Part I covers line graphs and their properties, while Part II looks at features that apply specifically to directed graphs, and Part III presents generalizations and variations of both line graphs and line digraphs. Line Graphs and Line Digraphs is the first comprehensive monograph on the topic. With minimal prerequisites, the book is accessible to most mathematicians and computer scientists who have had an introduction graph theory, and will be a valuable reference for researchers working in graph theory and related fields.
Download or read book Generalized Line Graphs written by Mohra Abdullah Alqahtani and published by . This book was released on 2018 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: With every nonempty graph, there are associated many graphs. One of the best known and most studied of these is the line graph L (G) of a graph G, whose vertices are the edges of G and where two vertices of L (G) are adjacent if the corresponding edges of G are adjacent. This concept was implicitly introduced by Whitney in 1932. Over the years, characterizations of graphs that are line graphs have been given, as well as graphs whose line graphs have some specified property. For example, Beineke characterized graphs that are line graphs by forbidding certain graphs that can be subgroups. Sedlacek characterized those graphs whose line graph is planar. Harary and Nash-Williams characterized those graphs whose line graph is Hamiltonian. Chartrand and Wall proved that if G is a connected graph all of whose vertices have degree 3 or more, then, although L(G) may not be Hamiltonian, the line graph of L(G) must be Hamiltonian. Over the years, various generalizations of line graphs have been introduced and studied by many. Among them are Schwenk graphs and k-line graphs introduced in 2015 and 2016 here at Western Michigan University. This study introduces a generalization of line graphs and discusses several well-known structural properties of this class of graphs. Furthermore, it establishes a number of characterizations of connected graphs whose generalized line graphs possess some prescribed graph structure.
Download or read book Spectral Generalizations of Line Graphs written by Dragoš M. Cvetković and published by . This book was released on 2004 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: An important resource for all researchers with an interest in algebraic graph theory.
Download or read book Spectral Generalizations of Line Graphs written by Dragoš M. Cvetković and published by . This book was released on 2014-05-14 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Line graphs have the property that their least eigenvalue is greater than, or equal to, -2, a property shared by generalized line graphs and a finite number of so-called exceptional graphs. This book deals with all these families of graphs in the context of their spectral properties. Technical descriptions of these graphs are included in the appendices, while the bibliography provides over 250 references. It will be an important resource for all researchers with an interest in algebraic graph theory.
Download or read book Line Graphs and Generalizations written by Erich Prisner and published by . This book was released on 1995 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Subgraph Transformations written by Blayne Earl Carroll and published by . This book was released on 1995 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Graph Classes written by Andreas Brandstadt and published by SIAM. This book was released on 1999-01-01 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: The definitive encyclopedia for the literature on graph classes.
Download or read book Some Root Level Modifications in Interval Valued Fuzzy Graphs and Their Generalizations Including Neutrosophic Graphs written by Naeem Jan and published by Infinite Study. This book was released on with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fuzzy graphs (FGs) and their generalizations have played an essential role in dealing with real-life problems involving uncertainties. The goal of this article is to show some serious flaws in the existing definitions of several root-level generalized FG structures with the help of some counterexamples. To achieve this, first, we aim to improve the existing definition for interval-valued FG, interval-valued intuitionistic FG and their complements, as these existing definitions are not well-defined; i.e., one can obtain some senseless intervals using the existing definitions. The limitations of the existing definitions and the validity of the new definitions are supported with some examples.
Download or read book Line Graphs and Line Digraphs written by Lowell W. Beineke and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present era dominated by computers, graph theory has come into its own as an area of mathematics, prominent for both its theory and its applications. One of the richest and most studied types of graph structures is that of the line graph, where the focus is more on the edges of a graph than on the vertices. A subject worthy of exploration in itself, line graphs are closely connected to other areas of mathematics and computer science. This book is unique in its extensive coverage of many areas of graph theory applicable to line graphs. The book has three parts. Part I covers line graphs and their properties, while Part II looks at features that apply specifically to directed graphs, and Part III presents generalizations and variations of both line graphs and line digraphs. Line Graphs and Line Digraphs is the first comprehensive monograph on the topic. With minimal prerequisites, the book is accessible to most mathematicians and computer scientists who have had an introduction graph theory, and will be a valuable reference for researchers working in graph theory and related fields.
Download or read book Structures of Derived Graphs written by Khawlah Hamad Alhulwah and published by . This book was released on 2017 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most familiar derived graphs are line graphs. The line graph L(G) of a graph G is the graph whose vertices are the edges of G where two vertices of L(G) are adjacent if and only if the corresponding edges of G are adjacent. One of the best- known results on the structure of line graphs deals with forbidden subgraphs by Beineke. A characterization of graphs whose line graph is Hamiltonian is due to Harary and Nash-Williams. Iterated line graphs of almost all connected graphs were shown to be Hamiltonian by Chartrand. The girth of a graph G is the length of a smallest cycle of G. An r-regular graph of girth g of minimum order is called a cage. Another class of derived graphs having a connection with cages was introduced by Schwenk. For a graph G having girth 2k + 1, the Schwenk graph G* of G has the set of all (k + 1)-paths as its vertex set where two vertices P and Q are adjacent in G* if and only if P and Q have only an end-vertex in common and the vertices of P and Q induce a (2k + 1)-cycle. In this work, we introduce two new classes of derived graphs, called l -line graphs and Z-graphs. The concept of l -line graphs is a generalization of line graphs and Schwenk graphs, while the Z-graphs provide a different view of certain line graphs. We primarily study the structures of these derived graphs. Results, conjectures and problems on the structural properties such that connectedness, decompositions, Hamiltonicity and planarity of these graphs are presented.
Download or read book Spectra of Graphs written by Andries E. Brouwer and published by Springer Science & Business Media. This book was released on 2011-12-17 with total page 254 pages. 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.
Download or read book Graph Representation Learning written by William L. William L. Hamilton and published by Springer Nature. This book was released on 2022-06-01 with total page 141 pages. 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.
Download or read book Generalized Connectivity of Graphs written by Xueliang Li and published by Springer. This book was released on 2016-06-30 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations with the Steiner tree packing problem and generalizations of connectivity. This book enables graduate students to understand and master a segment of graph theory and combinatorial optimization. Researchers in graph theory, combinatorics, combinatorial optimization, probability, computer science, discrete algorithms, complexity analysis, network design, and the information transferring models will find this book useful in their studies.
Download or read book Mathematical Combinatorics Vol 1 2011 written by Linfan Mao and published by Infinite Study. This book was released on with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Supermagic Coverings of Some Simple Graphs, Super Fibonacci Graceful Labeling of Some Special Class of Graphs, Surface Embeddability of Graphs via Tree-travels, and similar topics. Contributors: M.A. Perumal, S. Navaneethakrishnan, A. Nagarajan, Linfan Mao, S. Ersoy, M. Akyigit, M. Tosun, Keke Wang, Rongxia Hao, Jianbing Liu, P. Siva Kota Reddy, B. Prashanth, Kavita S. Permi, and others.
Download or read book International Journal of Mathematical Combinatorics Volume 1 2011 written by Linfan Mao and published by Infinite Study. This book was released on with total page 140 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. The International J. Mathematical Combinatorics is a fully refereed international journal, 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, Smarandache multi-spaces, Smarandache geometries, non-Euclidean geometry, topology and their applications to other sciences.
Download or read book Combinatorial Optimization written by B. N. Waphare and published by Alpha Science Int'l Ltd.. This book was released on 2004 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributed papers presented at a national workshop held at Dept.of Mathematics, University of Pune.
