[PDF] Graph Symmetry eBook

Author : Gena Hahn
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 29,75 MB
Release : 2013-03-14
Category : Mathematics
ISBN : 9401589372

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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 : Ted Dobson
Publisher : Cambridge University Press
Page : 527 pages
File Size : 21,69 MB
Release : 2022-05-12
Category : Language Arts & Disciplines
ISBN : 1108429068

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

Author : Jose M. Rodriguez
Publisher : MDPI
Page : 340 pages
File Size : 50,19 MB
Release : 2019-03-14
Category : Mathematics
ISBN : 303897658X

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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
Publisher : Cambridge University Press
Page : 528 pages
File Size : 50,31 MB
Release : 2022-05-12
Category : Mathematics
ISBN : 1108643620

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This is the first full-length book on the major theme of symmetry in graphs. Forming part of algebraic graph theory, this fast-growing field is concerned with the study of highly symmetric graphs, particularly vertex-transitive graphs, and other combinatorial structures, primarily by group-theoretic techniques. In practice the street goes both ways and these investigations shed new light on permutation groups and related algebraic structures. The book assumes a first course in graph theory and group theory but no specialized knowledge of the theory of permutation groups or vertex-transitive graphs. It begins with the basic material before introducing the field's major problems and most active research themes in order to motivate the detailed discussion of individual topics that follows. Featuring many examples and over 450 exercises, it is an essential introduction to the field for graduate students and a valuable addition to any algebraic graph theorist's bookshelf.

Author : István Hargittai
Publisher : Elsevier
Page : 1068 pages
File Size : 34,95 MB
Release : 2014-05-23
Category : Science
ISBN : 1483149528

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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
Publisher : MDPI
Page : 144 pages
File Size : 50,90 MB
Release : 2019-10-30
Category : Mathematics
ISBN : 3039217208

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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 : Petra Mutzel
Publisher : Springer
Page : 537 pages
File Size : 47,73 MB
Release : 2003-07-31
Category : Computers
ISBN : 3540458484

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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 : 48,5 MB
Release : 2018-07-09
Category : Mathematics
ISBN : 3038424986

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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 : 473 pages
File Size : 23,5 MB
Release : 2013-05-16
Category : Science
ISBN : 3709115655

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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 : Angel Garrido
Publisher : MDPI
Page : 458 pages
File Size : 26,75 MB
Release : 2020-03-05
Category : Mathematics
ISBN : 3039281909

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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.