Integral Trees: Subtree Depth and Diameter Walter G. Kropatsch1, Yll Haxhimusa1, and Zygmunt Pizlo2 1,⋆ Vienna University of Technology, ... Integral features capture important properties of these regions and the associated trees.
Author: Reinhard Klette
Publisher: Springer Science & Business Media
This volume presents the proceedings of the 10th International Workshop on Combinatorial Image Analysis, held December 1–3, 2004, in Auckland, New Zealand. Prior meetings took place in Paris (France, 1991), Ube (Japan, 1992), Washington DC (USA, 1994), Lyon (France, 1995), Hiroshima (Japan, 1997), Madras (India, 1999), Caen (France, 2000), Philadelphia (USA, 2001), and - lermo (Italy, 2003). For this workshop we received 86 submitted papers from 23 countries. Each paper was evaluated by at least two independent referees. We selected 55 papers for the conference. Three invited lectures by Vladimir Kovalevsky (Berlin), Akira Nakamura (Hiroshima), and Maurice Nivat (Paris) completed the program. Conference papers are presented in this volume under the following topical part titles: discrete tomography (3 papers), combinatorics and computational models (6), combinatorial algorithms (6), combinatorial mathematics (4), d- ital topology (7), digital geometry (7), approximation of digital sets by curves and surfaces (5), algebraic approaches (5), fuzzy image analysis (2), image s- mentation (6), and matching and recognition (7). These subjects are dealt with in the context of digital image analysis or computer vision.
M. Belii Math 10 (2003) 9–15 Li, X.L., Lin, G.N.: On Trees with Integer Eigenvalues. Kexue Tongbao (Chinese Science Bulletin) 32 (11) (1987) 813–816 (in Chinese), or On Integral Trees Problems. Kexue Tongbao (English Ed.) 33 (10) (1988) ...
Author: Jin Akiyama
This book constitutes the thoroughly refereed post-proceedings of the 7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005, held in Tianjin, China, as well as in Xi'an, China, in November 2005. The 30 revised full papers address all current issues in discrete algorithmic geometry, combinatorics and graph theory.
The Integral Trees fully makes up for a certain modichohum of laurel-resting that had crept into his work meanwhile; it zaps right along, combining expert action-plotting with a steady proliferation of science-borne extrapolation.
Author: Algis Budrys
Category: Science fiction
Consists of book reviews and essays written for The magazine of fantasy and science fiction.
It is worth mentioning that problem ( a ) is unsolved even for trees : the known results concern integral trees of diameter less than 11. Concerning ( b ) , observe that the family of integral graphs is closed under the NEPS operation ...
Author: Dragoš Cvetkovic
Publisher: Cambridge University Press
Introduction -- Forbidden subgraphs -- Root systems -- Regular graphs -- Star complements -- The Maximal exceptional graphs -- Miscellaneous results.
Every line graph L(K.) is integral. In particular, the octahedron is integral since it is L(K4) . Furthermore the Pertersen graph P is seen to be integral by applying both Corollary 1 and Corollary 6 since P = L(K5) • 3. INTEGRAL TREES ...
Integral trees have been studied in [WAT2} and (WASC1]. It was proved in [WAT2) that the only integral tree with a complete matching is K2. Also a family of integral trees of diameter 4 has been constructed. All integral trees ...
Author: D.M. Cvetkovic
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.
Larry Niven's The Integral Trees is good oldfashioned science fiction about people living somewhere with weird physics—in a cluster of floating trees and things. I remember enjoying it on a long train journey. It won the Locus Award.
Author: Jo Walton
Category: Literary Criticism
Engaged, passionate, and consistently entertaining, An Informal History of the Hugos is a book about the renowned science fiction award for the many who enjoyed Jo Walton's previous collection of writing from Tor.com, the Locus Award-winning What Makes This Book So Great. The Hugo Awards, named after pioneer science-fiction publisher Hugo Gernsback, and voted on by members of the World Science Fiction Society, have been presented since 1953. They are widely considered the most prestigious awards in science fiction. Between 2010 and 2013, Jo Walton wrote a series of posts for Tor.com, surveying the Hugo finalists and winners from the award's inception up to the year 2000. Her contention was that each year's full set of finalists generally tells a meaningful story about the state of science fiction at that time. Walton's cheerfully opinionated and vastly well-informed posts provoked valuable conversation among the field's historians. Now these posts, lightly revised, have been gathered into this book, along with a small selection of the comments posted by SF luminaries such as Rich Horton, Gardner Dozois, and David G. Hartwell. "A remarkable guided tour through the field—a kind of nonfiction companion to Among Others. It's very good. It's great."—New York Times bestselling author Cory Doctorow, Boing Boing on What Makes This Book So Great At the Publisher's request, this title is being sold without Digital Rights Management Software (DRM) applied.
Proof The constant term of the characteristic polynomial of a tree is, up to sign, the number of perfect matchings. ... D For a long time it has been an open question whether there exist integral trees of arbitrarily large diameter.
Author: Andries E. Brouwer
Publisher: Springer Science & Business Media
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.
Integral. trees. of. odd. diameters. By a News Reporter-Staff News Editor at Journal of Mathematics — Fresh data on ... from the School of Mathematics, “Recently, Csikvari proved the existence of integral trees of any even diameter.
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