Download or read book The Harary Index of a Graph written by Kexiang Xu and published by Springer. This book was released on 2015-01-12 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to focus on the topological index, the Harary index, of a graph, including its mathematical properties, chemical applications and some related and attractive open problems. This book is dedicated to Professor Frank Harary (1921—2005), the grandmaster of graph theory and its applications. It has be written by experts in the field of graph theory and its applications. For a connected graph G, as an important distance-based topological index, the Harary index H(G) is defined as the sum of the reciprocals of the distance between any two unordered vertices of the graph G. In this book, the authors report on the newest results on the Harary index of a graph. These results mainly concern external graphs with respect to the Harary index; the relations to other topological indices; its properties and applications to pure graph theory and chemical graph theory; and two significant variants, i.e., additively and multiplicatively weighted Harary indices. In the last chapter, we present a number of open problems related to the Harary index. As such, the book will not only be of interest to graph researchers, but to mathematical chemists as well.
Download or read book Topological Indices and Related Descriptors in QSAR and QSPR written by James Devillers and published by CRC Press. This book was released on 2000-03-09 with total page 822 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological Indices and Related Descriptors in QSAR and QSPR reviews the state of the art in this field and highlights the important advances in the generation of descriptors calculated directly from the structure of molecules. This long-awaited comprehensive book provides all the necessary information to calculate and use these descriptors for deriving structure-activity and structure-property relationships. Written by leading experts in the field, this book discusses the physicochemical significance, strengths, and weaknesses of these indices and presents numerous examples of applications. This book will be a valuable reference for anyone involved in the use of QSAR and QSPR in the pharmaceutical, applied chemical, and environmental sciences. It is also suitable for use as a supplementary textbook on related graduate level courses.
Download or read book Mathematical Concepts in Organic Chemistry written by Ivan Gutman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book is an attempt to outline some, certainly not all, mathematical aspects of modern organic chemistry. We have focused our attention on topological, graph-theoretical and group-theoretical features of organic chemistry, Parts A, B and C. The book is directed to all those chemists who use, or who intend to use mathe matics in their work, and especially to graduate students. The level of our exposition is adjusted to the mathematical background of graduate students of chemistry and only some knowledge of elementary algebra and calculus is required from the readers of the book. Some less well-known. but still elementary mathematical facts are collected in Appendices 1-4. This, however, does not mean that the mathematical rigor and numerous tedious, but necessary technical details have been avoided. The authors' intention was to show the reader not only how the results of mathematical chemistry look, but also how they can be obtained. In accordance with this, Part 0 of the book contains a few selected advanced topics which should give the reader the flavour of the contemporary research in mathe matical organic chemistry. One of the authors (I.G.) was an Alexander von Humboldt fellow in 1985 when the main part of the book was written. He gratefully acknowledges the financial support of the Alexander von Humboldt Foundation which enabled his stay at the Max-Planck-Institut fUr Strahlenchemie in M iilheim and the writing of this book.
Download or read book Graphical Enumeration written by Frank Harary and published by Elsevier. This book was released on 2014-05-10 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graphical Enumeration deals with the enumeration of various kinds of graphs. Topics covered range from labeled enumeration and George Pólya's theorem to rooted and unrooted trees, graphs and digraphs, and power group enumeration. Superposition, blocks, and asymptotics are also discussed. A number of unsolved enumeration problems are presented. Comprised of 10 chapters, this book begins with an overview of labeled graphs, followed by a description of the basic enumeration theorem of Pólya. The next three chapters count an enormous variety of trees, graphs, and digraphs. The Power Group Enumeration Theorem is then described together with some of its applications, including the enumeration of self-complementary graphs and digraphs and finite automata. Two other chapters focus on the counting of superposition and blocks, while another chapter is devoted to asymptotic numbers that are developed for several different graphical structures. The book concludes with a comprehensive definitive list of unsolved graphical enumeration problems. This monograph will be of interest to both students and practitioners of mathematics.
Download or read book Fractional Graph Theory written by Edward R. Scheinerman and published by Courier Corporation. This book was released on 2013-04-29 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume explains the general theory of hypergraphs and presents in-depth coverage of fundamental and advanced topics: fractional matching, fractional coloring, fractional edge coloring, fractional arboricity via matroid methods, fractional isomorphism, and more. 1997 edition.
Download or read book New Directions in the Theory of Graphs written by Frank Harary and published by . This book was released on 1973 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Graph theoretical Matrices in Chemistry written by Du{uFFFD}anka Jane{uFFFD}ic and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Distance In Graphs written by Fred Buckley and published by Addison Wesley Publishing Company. This book was released on 1990-01-21 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Graph Theory written by Frank Harary and published by . This book was released on 1969 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Island Networks written by Per Hage and published by Cambridge University Press. This book was released on 1996-10-28 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using network models from graph theory, this book analyses the formation of Pacific island empires.
Download or read book Graphs and Matrices written by Ravindra B. Bapat and published by Springer. This book was released on 2014-09-19 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reorganized. Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory, it will also benefit readers in the sciences and engineering.
Download or read book Crossing Numbers of Graphs written by Marcus Schaefer and published by CRC Press. This book was released on 2018-01-02 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Crossing Numbers of Graphs is the first book devoted to the crossing number, an increasingly popular object of study with surprising connections. The field has matured into a large body of work, which includes identifiable core results and techniques. The book presents a wide variety of ideas and techniques in topological graph theory, discrete geometry, and computer science. The first part of the text deals with traditional crossing number, crossing number values, crossing lemma, related parameters, computational complexity, and algorithms. The second part includes the rich history of alternative crossing numbers, the rectilinear crossing number, the pair crossing number, and the independent odd crossing number.It also includes applications of the crossing number outside topological graph theory. Aimed at graduate students and professionals in both mathematics and computer science The first book of its kind devoted to the topic Authored by a noted authority in crossing numbers
Download or read book Discriminants Resultants and Multidimensional Determinants written by Israel M. Gelfand and published by Springer Science & Business Media. This book was released on 2009-05-21 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book revives and vastly expands the classical theory of resultants and discriminants. Most of the main new results of the book have been published earlier in more than a dozen joint papers of the authors. The book nicely complements these original papers with many examples illustrating both old and new results of the theory."—Mathematical Reviews
Download or read book Spectra of Graphs written by Dragoš M. Cvetković and published by . This book was released on 1980 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of graph spectra can, in a way, be considered as an attempt to utilize linear algebra including, in particular, the well-developed theory of matrices for the purposes of graph theory and its applications. to the theory of matrices; on the contrary, it has its own characteristic features and specific ways of reasoning fully justifying it to be treated as a theory in its own right.
Download or read book Applying Graph Theory in Ecological Research written by Mark R.T. Dale and published by Cambridge University Press. This book was released on 2017-11-09 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book clearly describes the many applications of graph theory to ecological questions, providing instruction and encouragement to researchers.
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 331 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.
Download or read book An Atlas of Graphs written by Ronald C. Read and published by Mathematics. This book was released on 2004 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
