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Author : Bogdan Nica
ISBN : 3037191880
Genre : Eigenvalues
File Size : 49.5 MB
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"Spectral graph theory starts by associating matrices to graphs - notably, the adjacency matrix and the Laplacian matrix. The general theme is then, firstly, to compute or estimate the eigenvalues of such matrices, and secondly, to relate the eigenvalues to structural properties of graphs. As it turns out, the spectral perspective is a powerful tool. Some of its loveliest applications concern facts that are, in principle, purely graph theoretic or combinatorial. This text is an introduction to spectral graph theory, but it could also be seen as an invitation to algebraic graph theory. The first half is devoted to graphs, finite fields, and how they come together. This part provides an appealing motivation and context of the second, spectral, half. The text is enriched by many exercises and their solutions. The target audience are students from the upper undergraduate level onwards. We assume only a familiarity with linear algebra and basic group theory. Graph theory, finite fields, and character theory for abelian groups receive a concise overview and render the text essentially self-contained"--

Author : Jonathan L. Gross
ISBN : 0203490207
Genre : Mathematics
File Size : 81.9 MB
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The Handbook of Graph Theory is the most comprehensive single-source guide to graph theory ever published. Best-selling authors Jonathan Gross and Jay Yellen assembled an outstanding team of experts to contribute overviews of more than 50 of the most significant topics in graph theory-including those related to algorithmic and optimization approaches as well as "pure" graph theory. They then carefully edited the compilation to produce a unified, authoritative work ideal for ready reference. Designed and edited with non-experts in mind, the Handbook of Graph Theory makes information easy to find and easy to understand. The treatment of each topic includes lists of essential definitions and facts accompanied by examples, tables, remarks, and in some areas, conjectures and open problems. Each section contains a glossary of terms relevant to that topic and an extensive bibliography of references that collectively form an extensive guide to the primary research literature. The applications of graph theory are fast becoming ubiquitous. Whether your primary area of interest lies in mathematics, computer science, engineering, or operations research, this handbook holds the key to unlocking graph theory's intricacies, applications, and potential.

The tool for visualization is Microsoft Visual C++. This popular software has the standard C++ combined with the Microsoft Foundation Classes (MFC) libraries for Windows visualization. This book explains how to create a graph interactively, solve problems in graph theory with minimum number of C++ codes, and provide friendly interfaces that makes learning the topics an interesting one. Each topic in the book comes with working Visual C++ codes which can easily be adapted as solutions to various problems in science and engineering.

Author : D.M. Cvetkovic
ISBN : 0080867766
Genre : Mathematics
File Size : 84.62 MB
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The purpose of this volume is to review the results in spectral graph theory which have appeared since 1978. The problem of characterizing graphs with least eigenvalue -2 was one of the original problems of spectral graph theory. The techniques used in the investigation of this problem have continued to be useful in other contexts including forbidden subgraph techniques as well as geometric methods involving root systems. In the meantime, the particular problem giving rise to these methods has been solved almost completely. This is indicated in Chapter 1. The study of various combinatorial objects (including distance regular and distance transitive graphs, association schemes, and block designs) have made use of eigenvalue techniques, usually as a method to show the nonexistence of objects with certain parameters. The basic method is to construct a graph which contains the structure of the combinatorial object and then to use the properties of the eigenvalues of the graph. Methods of this type are given in Chapter 2. Several topics have been included in Chapter 3, including the relationships between the spectrum and automorphism group of a graph, the graph isomorphism and the graph reconstruction problem, spectra of random graphs, and the Shannon capacity problem. Some graph polynomials related to the characteristic polynomial are described in Chapter 4. These include the matching, distance, and permanental polynomials. Applications of the theory of graph spectra to Chemistry and other branches of science are described from a mathematical viewpoint in Chapter 5. The last chapter is devoted to the extension of the theory of graph spectra to infinite graphs.

Non-linear image processing -- Color photo denoising via hue, saturation and intensity diffusion / Lei He and Chenyang Xu -- Examining the role of scale in the context of the non-local-means filter / Mehran Ebrahimi and Edward R. Vrscay -- Geometrical mutliscale noise resistant method of edge detection / Agnieszka Lisowska -- A simple, general model for the affine self-similarity of images / SImon K. Alexander, Edward R. Vrscay, and Satoshi Tsurumi -- Image and video coding and encryption -- Efficient bit-rate estimation for mode decision of H. 264 / AVC / Shuwei Sun and Shuming Chen -- Introducing a two dimensional measure for watermarking capacity in images / Farzin Yaghmaee and Mansour Jamzad -- Estimating the detectability of small lesions in high resolution MR compressed images / Juan Paz, Marlen Pérez, Iroel Miranda, and Peter Schelkens -- JPEG artifact removal using error distributions of linear coefficient estimates / Mika Inki --

Author : László Lovász
ISBN : UOM:39015037748343
Genre : Mathematics
File Size : 90.29 MB
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Good,No Highlights,No Markup,all pages are intact, Slight Shelfwear,may have the corners slightly dented, may have slight color changes/slightly damaged spine.