Graph Symmetry
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Graph Symmetry
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Author : Gena Hahn
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Graph Symmetry written by Gena Hahn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
The last decade has seen two parallel developments, one in computer science, the other in mathematics, both dealing with the same kind of combinatorial structures: networks with strong symmetry properties or, in graph-theoretical language, vertex-transitive graphs, in particular their prototypical examples, Cayley graphs. In the design of large interconnection networks it was realised that many of the most fre quently used models for such networks are Cayley graphs of various well-known groups. This has spawned a considerable amount of activity in the study of the combinatorial properties of such graphs. A number of symposia and congresses (such as the bi-annual IWIN, starting in 1991) bear witness to the interest of the computer science community in this subject. On the mathematical side, and independently of any interest in applications, progress in group theory has made it possible to make a realistic attempt at a complete description of vertex-transitive graphs. The classification of the finite simple groups has played an important role in this respect.
Symmetry In Graphs
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Author : Ted Dobson
language : en
Publisher: Cambridge University Press
Release Date : 2022-05-12
Symmetry In Graphs written by Ted Dobson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-12 with Language Arts & Disciplines categories.
The first full-length book on the theme of symmetry in graphs, a fast-growing topic in algebraic graph theory.
Symmetries Of Nonlinear Pdes On Metric Graphs And Branched Networks
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Author : Dmitry Pelinovsky
language : en
Publisher: MDPI
Release Date : 2019-10-30
Symmetries Of Nonlinear Pdes On Metric Graphs And Branched Networks written by Dmitry Pelinovsky and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-30 with Mathematics categories.
This Special Issue focuses on recent progress in a new area of mathematical physics and applied analysis, namely, on nonlinear partial differential equations on metric graphs and branched networks. Graphs represent a system of edges connected at one or more branching points (vertices). The connection rule determines the graph topology. When the edges can be assigned a length and the wave functions on the edges are defined in metric spaces, the graph is called a metric graph. Evolution equations on metric graphs have attracted much attention as effective tools for the modeling of particle and wave dynamics in branched structures and networks. Since branched structures and networks appear in different areas of contemporary physics with many applications in electronics, biology, material science, and nanotechnology, the development of effective modeling tools is important for the many practical problems arising in these areas. The list of important problems includes searches for standing waves, exploring of their properties (e.g., stability and asymptotic behavior), and scattering dynamics. This Special Issue is a representative sample of the works devoted to the solutions of these and other problems.
Graph Drawing
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Author : Petra Mutzel
language : en
Publisher: Springer
Release Date : 2003-07-31
Graph Drawing written by Petra Mutzel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-31 with Computers categories.
This book constitutes the thoroughly refereed post-proceedings of the 9th International Symposium on Graph Drawing, GD 2001, held in Vienna, Austria, in September 2001. The 32 revised full papers presented were carefully reviewed and selected from 66 paper submissions. Also included are a corrected version of a paper from the predecessor volume, short reports on the software systems exhibition, two papers of the special session on graph exchange formats, and a report on the annual graph drawing contests. The papers are organized in topical sections on hierarchical drawing, planarity, crossing theory, compaction, planar graphs, symmetries, interactive drawing, representations, aesthetics, 2D- and 3D-embeddings, data visualization, floor planning, and planar drawing.
Algebraic Graph Theory
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Author : Norman Biggs
language : en
Publisher: Cambridge University Press
Release Date : 1993
Algebraic Graph Theory written by Norman Biggs and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
This is a substantial revision of a much-quoted monograph, first published in 1974. The structure is unchanged, but the text has been clarified and the notation brought into line with current practice. A large number of 'Additional Results' are included at the end of each chapter, thereby covering most of the major advances in the last twenty years. Professor Biggs' basic aim remains to express properties of graphs in algebraic terms, then to deduce theorems about them. In the first part, he tackles the applications of linear algebra and matrix theory to the study of graphs; algebraic constructions such as adjacency matrix and the incidence matrix and their applications are discussed in depth. There follows an extensive account of the theory of chromatic polynomials, a subject which has strong links with the 'interaction models' studied in theoretical physics, and the theory of knots. The last part deals with symmetry and regularity properties. Here there are important connections with other branches of algebraic combinatorics and group theory. This new and enlarged edition this will be essential reading for a wide range of mathematicians, computer scientists and theoretical physicists.
Handbook Of Graph Drawing And Visualization
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Author : Roberto Tamassia
language : en
Publisher: CRC Press
Release Date : 2013-08-19
Handbook Of Graph Drawing And Visualization written by Roberto Tamassia and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-19 with Mathematics categories.
Get an In-Depth Understanding of Graph Drawing Techniques, Algorithms, Software, and Applications The Handbook of Graph Drawing and Visualization provides a broad, up-to-date survey of the field of graph drawing. It covers topological and geometric foundations, algorithms, software systems, and visualization applications in business, education, science, and engineering. Each chapter is self-contained and includes extensive references. The first several chapters of the book deal with fundamental topological and geometric concepts and techniques used in graph drawing, such as planarity testing and embedding, crossings and planarization, symmetric drawings, and proximity drawings. The following chapters present a large collection of algorithms for constructing drawings of graphs, including tree, planar straight-line, planar orthogonal and polyline, spine and radial, circular, rectangular, hierarchical, and three-dimensional drawings as well as labeling algorithms, simultaneous embeddings, and force-directed methods. The book then introduces the GraphML language for representing graphs and their drawings and describes three software systems for constructing drawings of graphs: OGDF, GDToolkit, and PIGALE. The final chapters illustrate the use of graph drawing methods in visualization applications for biological networks, computer security, data analytics, education, computer networks, and social networks. Edited by a pioneer in graph drawing and with contributions from leaders in the graph drawing research community, this handbook shows how graph drawing and visualization can be applied in the physical, life, and social sciences. Whether you are a mathematics researcher, IT practitioner, or software developer, the book will help you understand graph drawing methods and graph visualization systems, use graph drawing techniques in your research, and incorporate graph drawing solutions in your products.
Graph Drawing
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Author : Jan Kratochvil
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-12-22
Graph Drawing written by Jan Kratochvil and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-12-22 with Computers categories.
This book constitutes the thoroughly refereed post-proceedings of the 7th International Symposium on Graph Drawing, GD '99, held in Stirin Castle, Czech Republic, in September 1999. The 38 revised full papers presented together with three invited contributions, two posters, and a report on the graph drawing contest were carefully reviewed and selected from 59 submissions. Among the topics addressed are orthogonality, levels, clusters, drawing, planarity, applications, symmetry, representations, and proximity and trees.
Graph Drawing
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Author : Jan Kratochvil
language : en
Publisher: Springer
Release Date : 2003-06-26
Graph Drawing written by Jan Kratochvil and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-26 with Computers categories.
The range of issues considered in graph drawing includes algorithms, graph theory, geometry, topology, order theory, graphic languages, perception, app- cations, and practical systems. Much research is motivated by applications to systems for viewing and interacting with graphs. The interaction between th- retical advances and implemented solutions is an important part of the graph drawing eld. The annually organized graph drawing symposium is a forum for researchers, practitioners, developers, and users working on all aspects of graph visualization and representations. The preceding symposia were held in M- treal (GD’98), Rome (GD’97), Berkeley (GD’96), Passau (GD’95), Princeton (GD’94), and Paris (GD’93). The Seventh International Symposium on Graph Drawing GD’99 was or- nized at Sti r n Castle, in the vicinity of Prague, Czech Republic. This baroque castle recently restored as a hotel and conference center provided a secluded place for the participants, who made good use of the working atmosphere of the conference. In total the symposium had 83 registered participants from 16 countries.
Symmetry In Crystallography
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Author : Paolo Radaelli
language : en
Publisher: Oxford University Press
Release Date : 2011-09-23
Symmetry In Crystallography written by Paolo Radaelli and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-23 with Science categories.
This book presents the reader with a fresh and unconventional approach to teaching crystallographic symmetry. Whereas traditional crystallography textbooks make a heavy use of algebra and rapidly become very technical, this book adopts in the first few chapters a 'pictorial' approach based on the symmetry diagrams of the International Tables for Crystallography. Readers are led step-by-step through simple 'frieze' and 'wallpaper' patterns, with many examples from the visual arts. At the end of chapter 3 they should be able to identify and analyse all these simple symmetries and apply to them the nomenclature and symbols of the International Tables. Mathematical formalism is introduced later on in the book, and by that time the reader will have gained a solid intuitive grasp of the subject matter. This book will provide graduate students, advanced undergraduate students and practitioners in physics, chemistry, earth sciences and structural biology with a solid foundation to master the International Tables of Crystallography, and to understand the relevant literature.
Discrete Mathematics And Symmetry
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Author : Angel Garrido
language : en
Publisher: MDPI
Release Date : 2020-03-05
Discrete Mathematics And Symmetry written by Angel Garrido and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-05 with Mathematics categories.
Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group.