Graph Symmetry

Author : Gena Hahn,Gert Sabidussi
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 43,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401589376

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Graph Symmetry by Gena Hahn,Gert Sabidussi Pdf

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.

Author : Gareth A. Jones,Ilia Ponomarenko,Jozef Širáň
Publisher : Springer Nature
Page : 234 pages
File Size : 52,5 Mb
Release : 2020-01-10
Category : Mathematics
ISBN : 9783030328085

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Isomorphisms, Symmetry and Computations in Algebraic Graph Theory by Gareth A. Jones,Ilia Ponomarenko,Jozef Širáň Pdf

This book consists of a selection of peer-reviewed contributions to the Workshop on Algebraic Graph Theory that took place in Pilsen, Czech Republic in October 2016. Primarily intended for early career researchers, it presents eight self-contained articles on a selection of topics within algebraic combinatorics, ranging from association schemes to symmetries of graphs and isomorphism testing. Algebraic combinatorics is a compelling mathematical discipline based on the powerful interplay of algebraic and combinatorial methods. Algebraic interpretation of combinatorial structures (such as symmetry or regularity) has often led to enlightening discoveries and powerful results, while discrete and combinatorial structures have given rise to new algebraic structures that have found valuable applications. In addition to these original research contributions, the reader will find a survey linking numerous threads in algebraic combinatorics, and an extensive tutorial showcasing the universality of algebraic methods in the study of combinatorial structures.

Author : Jose M. Rodriguez
Publisher : MDPI
Page : 340 pages
File Size : 41,9 Mb
Release : 2019-03-14
Category : Mathematics
ISBN : 9783038976585

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Symmetry in Graph Theory by Jose M. Rodriguez Pdf

This book contains the successful invited submissions to a Special Issue of Symmetry on the subject of “Graph Theory”. Although symmetry has always played an important role in Graph Theory, in recent years, this role has increased significantly in several branches of this field, including but not limited to Gromov hyperbolic graphs, the metric dimension of graphs, domination theory, and topological indices. This Special Issue includes contributions addressing new results on these topics, both from a theoretical and an applied point of view.

Author : Ted Dobson,Aleksander Malnič,Dragan Marušič
Publisher : Cambridge University Press
Page : 527 pages
File Size : 53,8 Mb
Release : 2022-05-12
Category : Language Arts & Disciplines
ISBN : 9781108429061

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Symmetry in Graphs by Ted Dobson,Aleksander Malnič,Dragan Marušič Pdf

The first full-length book on the theme of symmetry in graphs, a fast-growing topic in algebraic graph theory.

Author : István Hargittai
Publisher : Elsevier
Page : 1060 pages
File Size : 46,7 Mb
Release : 2014-05-23
Category : Science
ISBN : 9781483149523

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Symmetry by István Hargittai Pdf

International Series in Modern Applied Mathematics and Computer Science, Volume 10: Symmetry: Unifying Human Understanding provides a tremendous scope of “symmetry , covering subjects from fractals through court dances to crystallography and literature. This book discusses the limits of perfection, symmetry as an aesthetic factor, extension of the Neumann-Minnigerode-Curie principle, and symmetry of point imperfections in solids. The symmetry rules for chemical reactions, matching and symmetry of graphs, mosaic patterns of H. J. Woods, and bilateral symmetry in insects are also elaborated. This text likewise covers the crystallographic patterns, Milton's mathematical symbol of theodicy, symmetries of soap films, and gapon formalism. This volume is a good source for researchers and specialists concerned with symmetry.

Author : Dmitry Pelinovsky,Diego Noja
Publisher : MDPI
Page : 144 pages
File Size : 47,5 Mb
Release : 2019-10-30
Category : Mathematics
ISBN : 9783039217205

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Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks by Dmitry Pelinovsky,Diego Noja Pdf

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.

Author : Angel Garrido
Publisher : MDPI
Page : 458 pages
File Size : 44,9 Mb
Release : 2020-03-05
Category : Mathematics
ISBN : 9783039281909

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Discrete Mathematics and Symmetry by Angel Garrido Pdf

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.

Author : Petra Mutzel,Michael Jünger,Sebastian Leipert
Publisher : Springer
Page : 528 pages
File Size : 46,6 Mb
Release : 2003-07-31
Category : Computers
ISBN : 9783540458487

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Graph Drawing by Petra Mutzel,Michael Jünger,Sebastian Leipert Pdf

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.

Author : Angel Garrido
Publisher : MDPI
Page : 509 pages
File Size : 54,8 Mb
Release : 2018-07-09
Category : Electronic book
ISBN : 9783038424987

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Symmetry Measures on Complex Networks by Angel Garrido Pdf

This book is a printed edition of the Special Issue "Symmetry Measures on Complex Networks" that was published in Symmetry

Author : Ali Kaveh
Publisher : Springer Science & Business Media
Page : 463 pages
File Size : 50,6 Mb
Release : 2013-05-16
Category : Science
ISBN : 9783709115657

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Optimal Analysis of Structures by Concepts of Symmetry and Regularity by Ali Kaveh Pdf

Optimal analysis is defined as an analysis that creates and uses sparse, well-structured and well-conditioned matrices. The focus is on efficient methods for eigensolution of matrices involved in static, dynamic and stability analyses of symmetric and regular structures, or those general structures containing such components. Powerful tools are also developed for configuration processing, which is an important issue in the analysis and design of space structures and finite element models. Different mathematical concepts are combined to make the optimal analysis of structures feasible. Canonical forms from matrix algebra, product graphs from graph theory and symmetry groups from group theory are some of the concepts involved in the variety of efficient methods and algorithms presented. The algorithms elucidated in this book enable analysts to handle large-scale structural systems by lowering their computational cost, thus fulfilling the requirement for faster analysis and design of future complex systems. The value of the presented methods becomes all the more evident in cases where the analysis needs to be repeated hundreds or even thousands of times, as for the optimal design of structures by different metaheuristic algorithms. The book is of interest to anyone engaged in computer-aided analysis and design and software developers in this field. Though the methods are demonstrated mainly through skeletal structures, continuum models have also been added to show the generality of the methods. The concepts presented are not only applicable to different types of structures but can also be used for the analysis of other systems such as hydraulic and electrical networks.

Author : Marston D. E. Conder,Antoine Deza,Asia Ivić Weiss
Publisher : Springer
Page : 333 pages
File Size : 42,9 Mb
Release : 2018-06-11
Category : Mathematics
ISBN : 9783319784342

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Discrete Geometry and Symmetry by Marston D. E. Conder,Antoine Deza,Asia Ivić Weiss Pdf

This book consists of contributions from experts, presenting a fruitful interplay between different approaches to discrete geometry. Most of the chapters were collected at the conference “Geometry and Symmetry” in Veszprém, Hungary from 29 June to 3 July 2015. The conference was dedicated to Károly Bezdek and Egon Schulte on the occasion of their 60th birthdays, acknowledging their highly regarded contributions in these fields. While the classical problems of discrete geometry have a strong connection to geometric analysis, coding theory, symmetry groups, and number theory, their connection to combinatorics and optimization has become of particular importance. The last decades have seen a revival of interest in discrete geometric structures and their symmetry. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory and geometry, combinatorial group theory, and hyperbolic geometry and topology. This book contains papers on new developments in these areas, including convex and abstract polytopes and their recent generalizations, tiling and packing, zonotopes, isoperimetric inequalities, and on the geometric and combinatorial aspects of linear optimization. The book is a valuable resource for researchers, both junior and senior, in the field of discrete geometry, combinatorics, or discrete optimization. Graduate students find state-of-the-art surveys and an open problem collection.

Author : Cynthia Y. Young
Publisher : John Wiley & Sons
Page : 1207 pages
File Size : 45,8 Mb
Release : 2010-01-19
Category : Mathematics
ISBN : 9780471756842

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Precalculus by Cynthia Y. Young Pdf

Engineers looking for an accessible approach to calculus will appreciate Young’s introduction. The book offers a clear writing style that helps reduce any math anxiety they may have while developing their problem-solving skills. It incorporates Parallel Words and Math boxes that provide detailed annotations which follow a multi-modal approach. Your Turn exercises reinforce concepts by allowing them to see the connection between the exercises and examples. A five-step problem solving method is also used to help engineers gain a stronger understanding of word problems.

Author : Paolo Radaelli
Publisher : Oxford University Press
Page : 141 pages
File Size : 41,9 Mb
Release : 2011-09-22
Category : Mathematics
ISBN : 9780199550654

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Symmetry in Crystallography by Paolo Radaelli Pdf

A fresh approach to teaching crystallographic symmetry. Rather than being swamped by heavy algebraic notation, the reader is taken through a series of simple and beautiful examples from the visual arts, and taught how to analyse them employing the 'pictorial' diagrams used in the International Tables of Crystallography.

Author : Ali Reza Ashrafi,Mircea V. Diudea
Publisher : Springer
Page : 477 pages
File Size : 53,8 Mb
Release : 2016-08-16
Category : Technology & Engineering
ISBN : 9783319315843

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Distance, Symmetry, and Topology in Carbon Nanomaterials by Ali Reza Ashrafi,Mircea V. Diudea Pdf

This contributed volume is inspired by the seminal discovery and identification of C60. Starting with a comprehensive discussion featuring graphene based nanostructures, subsequent chapters include topological descriptions of matrices, polynomials and indices, and an extended analysis of the symmetry and topology of nanostructures. Carbon allotropes such as diamond and its connection to higher-dimensional spaces is explored along with important mathematical and topological considerations. Further topics covered include spontaneous symmetry breaking in graphene, polyhedral carbon structures, nanotube junction energetics, and cyclic polyines as relatives of nanotubes and fullerenes. This book is aimed at researchers active in the study of carbon materials science and technology.

Author : Anonim
Publisher : John Wiley & Sons
Page : 995 pages
File Size : 42,7 Mb
Release : 2021-06-21
Category : Electronic
ISBN : 9781119582946

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Young, Precalculus, Third Edition by Anonim Pdf