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| Author | : Zoran Stanić |
| Publisher | : Cambridge University Press |
| Total Pages | : 311 |
| Release | : 2015-07-23 |
| Genre | : Mathematics |
| ISBN | : 1107545978 |
This book explores the inequalities for eigenvalues of the six matrices associated with graphs. Includes the main results and selected applications.
| Author | : Hanjo Taubig |
| Publisher | : CRC Press |
| Total Pages | : 219 |
| Release | : 2017-02-03 |
| Genre | : Mathematics |
| ISBN | : 1498777791 |
The book reviews inequalities for weighted entry sums of matrix powers. Applications range from mathematics and CS to pure sciences. It unifies and generalizes several results for products and powers of sesquilinear forms derived from powers of Hermitian, positive-semidefinite, as well as nonnegative matrices. It shows that some inequalities are valid only in specific cases. How to translate the Hermitian matrix results into results for alternating powers of general rectangular matrices? Inequalities that compare the powers of the row and column sums to the row and column sums of the matrix powers are refined for nonnegative matrices. Lastly, eigenvalue bounds and derive results for iterated kernels are improved.
| Author | : Charles R. Johnson |
| Publisher | : Cambridge University Press |
| Total Pages | : 315 |
| Release | : 2018-02-12 |
| Genre | : Mathematics |
| ISBN | : 110709545X |
This book investigates the influence of the graph of a symmetric matrix on the multiplicities of its eigenvalues.
| Author | : Fan R. K. Chung |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 228 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 0821803158 |
This text discusses spectral graph theory.
| Author | : Türker Biyikoglu |
| Publisher | : Springer |
| Total Pages | : 121 |
| Release | : 2007-07-07 |
| Genre | : Mathematics |
| ISBN | : 3540735100 |
This fascinating volume investigates the structure of eigenvectors and looks at the number of their sign graphs ("nodal domains"), Perron components, and graphs with extremal properties with respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main methodology. Eigenvectors of graph Laplacians may seem a surprising topic for a book, but the authors show that there are subtle differences between the properties of solutions of Schrödinger equations on manifolds on the one hand, and their discrete analogs on graphs.
| Author | : W. H. Haemers |
| Publisher | : |
| Total Pages | : 122 |
| Release | : 1980 |
| Genre | : Combinatorial designs and configurations |
| ISBN | : |
| Author | : Ravindra B. Bapat |
| Publisher | : Springer |
| Total Pages | : 197 |
| Release | : 2014-09-19 |
| Genre | : Mathematics |
| ISBN | : 1447165691 |
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.
| Author | : L. Lovász |
| Publisher | : Elsevier |
| Total Pages | : 636 |
| Release | : 2014-06-28 |
| Genre | : Mathematics |
| ISBN | : 0080933092 |
The aim of this book is to introduce a range of combinatorial methods for those who want to apply these methods in the solution of practical and theoretical problems. Various tricks and techniques are taught by means of exercises. Hints are given in a separate section and a third section contains all solutions in detail. A dictionary section gives definitions of the combinatorial notions occurring in the book. Combinatorial Problems and Exercises was first published in 1979. This revised edition has the same basic structure but has been brought up to date with a series of exercises on random walks on graphs and their relations to eigenvalues, expansion properties and electrical resistance. In various chapters the author found lines of thought that have been extended in a natural and significant way in recent years. About 60 new exercises (more counting sub-problems) have been added and several solutions have been simplified.
| Author | : Peter Buser |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 473 |
| Release | : 2010-10-29 |
| Genre | : Mathematics |
| ISBN | : 0817649921 |
This monograph is a self-contained introduction to the geometry of Riemann Surfaces of constant curvature –1 and their length and eigenvalue spectra. It focuses on two subjects: the geometric theory of compact Riemann surfaces of genus greater than one, and the relationship of the Laplace operator with the geometry of such surfaces. Research workers and graduate students interested in compact Riemann surfaces will find here a number of useful tools and insights to apply to their investigations.
| Author | : Armen S. Asratian |
| Publisher | : Cambridge University Press |
| Total Pages | : 283 |
| Release | : 1998-07-13 |
| Genre | : Mathematics |
| ISBN | : 9780521593458 |
This is the first book which deals solely with bipartite graphs. Together with traditional material, the reader will also find many new and unusual results. Essentially all proofs are given in full; many of these have been streamlined specifically for this text. Numerous exercises of all standards have also been included. The theory is illustrated with many applications especially to problems in timetabling, Chemistry, Communication Networks and Computer Science. For the most part the material is accessible to any reader with a graduate understanding of mathematics. However, the book contains advanced sections requiring much more specialized knowledge, which will be of interest to specialists in combinatorics and graph theory.
