Symmetry In Graphs

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Graph Symmetry

Gena Hahn,Gert Sabidussi
Graph Symmetry Book PDF

Author : Gena Hahn,Gert Sabidussi
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 46,9 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.

Symmetry in Graphs

Edward Tauscher Dobson,Aleksander Malnič,Dragan Marušič
Symmetry in Graphs Book PDF

Author : Edward Tauscher Dobson,Aleksander Malnič,Dragan Marušič
Publisher : Unknown
Page : 128 pages
File Size : 40,6 Mb
Release : 2022
Category : MATHEMATICS
ISBN : 1108553990

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Symmetry in Graphs by Edward Tauscher Dobson,Aleksander Malnič,Dragan Marušič Pdf

"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 with 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"--

Symmetry in Graphs

Ted Dobson,Aleksander Malnič,Dragan Marušič
Symmetry in Graphs Book PDF

Author : Ted Dobson,Aleksander Malnič,Dragan Marušič
Publisher : Cambridge University Press
Page : 527 pages
File Size : 42,6 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.

Symmetry in Graph Theory

Jose M. Rodriguez
Symmetry in Graph Theory Book PDF

Author : Jose M. Rodriguez
Publisher : MDPI
Page : 340 pages
File Size : 45,5 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.

Zero-Symmetric Graphs

H. S. M. Coxeter,Roberto Frucht,David L. Powers
Zero Symmetric Graphs Book PDF

Author : H. S. M. Coxeter,Roberto Frucht,David L. Powers
Publisher : Academic Press
Page : 181 pages
File Size : 44,9 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483268781

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Zero-Symmetric Graphs by H. S. M. Coxeter,Roberto Frucht,David L. Powers Pdf

Zero-Symmetric Graphs: Trivalent Graphical Regular Representations of Groups describes the zero-symmetric graphs with not more than 120 vertices.The graphs considered in this text are finite, connected, vertex-transitive and trivalent. This book is organized into three parts encompassing 25 chapters. The first part reviews the different classes of zero-symmetric graphs, according to the number of essentially different edges incident at each vertex, namely, the S, T, and Z classes. The remaining two parts discuss the theorem and characteristics of type 1Z and 3Z graphs. These parts explore Cayley graphs of specific groups, including the parameters of Cayley graphs of groups. This book will prove useful to mathematicians, computer scientists, and researchers.

Isomorphisms, Symmetry and Computations in Algebraic Graph Theory

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

Author : Gareth A. Jones,Ilia Ponomarenko,Jozef Širáň
Publisher : Springer Nature
Page : 234 pages
File Size : 48,9 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.

Discrete Mathematics and Symmetry

Angel Garrido
Discrete Mathematics and Symmetry Book PDF

Author : Angel Garrido
Publisher : MDPI
Page : 458 pages
File Size : 40,7 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.

Distance-Regular Graphs

Andries E. Brouwer,Arjeh M. Cohen,Arnold Neumaier
Distance Regular Graphs Book PDF

Author : Andries E. Brouwer,Arjeh M. Cohen,Arnold Neumaier
Publisher : Springer Science & Business Media
Page : 513 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642743412

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Distance-Regular Graphs by Andries E. Brouwer,Arjeh M. Cohen,Arnold Neumaier Pdf

Ever since the discovery of the five platonic solids in ancient times, the study of symmetry and regularity has been one of the most fascinating aspects of mathematics. Quite often the arithmetical regularity properties of an object imply its uniqueness and the existence of many symmetries. This interplay between regularity and symmetry properties of graphs is the theme of this book. Starting from very elementary regularity properties, the concept of a distance-regular graph arises naturally as a common setting for regular graphs which are extremal in one sense or another. Several other important regular combinatorial structures are then shown to be equivalent to special families of distance-regular graphs. Other subjects of more general interest, such as regularity and extremal properties in graphs, association schemes, representations of graphs in euclidean space, groups and geometries of Lie type, groups acting on graphs, and codes are covered independently. Many new results and proofs and more than 750 references increase the encyclopaedic value of this book.

Symmetry

István Hargittai
Symmetry Book PDF

Author : István Hargittai
Publisher : Elsevier
Page : 1068 pages
File Size : 47,6 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.

Topics in Graph Automorphisms and Reconstruction

Josef Lauri,Raffaele Scapellato
Topics in Graph Automorphisms and Reconstruction Book PDF

Author : Josef Lauri,Raffaele Scapellato
Publisher : Cambridge University Press
Page : 207 pages
File Size : 41,7 Mb
Release : 2016-06-02
Category : Mathematics
ISBN : 9781316610442

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Topics in Graph Automorphisms and Reconstruction by Josef Lauri,Raffaele Scapellato Pdf

An in-depth coverage of selected areas of graph theory focusing on symmetry properties of graphs, ideal for beginners and specialists.

Discrete Geometry and Symmetry

Marston D. E. Conder,Antoine Deza,Asia Ivić Weiss
Discrete Geometry and Symmetry Book PDF

Author : Marston D. E. Conder,Antoine Deza,Asia Ivić Weiss
Publisher : Springer
Page : 333 pages
File Size : 51,6 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.

Incidence and Symmetry in Design and Architecture

Jenny A. Baglivo,Jack E. Graver
Incidence and Symmetry in Design and Architecture Book PDF

Author : Jenny A. Baglivo,Jack E. Graver
Publisher : Cambridge University Press
Page : 319 pages
File Size : 46,8 Mb
Release : 1983-03-31
Category : Mathematics
ISBN : 0521230438

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Incidence and Symmetry in Design and Architecture by Jenny A. Baglivo,Jack E. Graver Pdf

The initial purposes of this 1983 text were to develop mathematical topics relevant to the study of the incidence and symmetry structures of geometrical objects and to expand the reader's geometric intuition. The two fundamental mathematical topics employed in this endeavor are graph theory and the theory of transformation groups. Part I, Incidence, starts with two sections on the basics of graph theory and continues with a variety of specific applications of graph theory. Following this, the text becomes more theoretical; here graph theory is used to study surfaces other than the plane and the sphere. Part II, Symmetry, starts with a section on rigid motions or symmetries of the plane, which is followed by another on the classification of planar patterns. Additionally, an overview of symmetry in three-dimensional space is provided, along with a reconciliation of graph theory and group theory in a study of enumeration problems in geometry.

Rigidity and Symmetry

Robert Connelly,Asia Ivić Weiss,Walter Whiteley
Rigidity and Symmetry Book PDF

Author : Robert Connelly,Asia Ivić Weiss,Walter Whiteley
Publisher : Springer
Page : 378 pages
File Size : 42,6 Mb
Release : 2014-06-11
Category : Mathematics
ISBN : 9781493907816

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Rigidity and Symmetry by Robert Connelly,Asia Ivić Weiss,Walter Whiteley Pdf

This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures and to explore the interaction of geometry, algebra and combinatorics. Contributions present recent trends and advances in discrete geometry, particularly in the theory of polytopes. 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, classical geometry, hyperbolic geometry and topology. Overall, the book shows how researchers from diverse backgrounds explore connections among the various discrete structures with symmetry as the unifying theme. The volume will be a valuable source as an introduction to the ideas of both combinatorial and geometric rigidity theory and its applications, incorporating the surprising impact of symmetry. It will appeal to students at both the advanced undergraduate and graduate levels, as well as post docs, structural engineers and chemists.

Optimal Analysis of Structures by Concepts of Symmetry and Regularity

Ali Kaveh
Optimal Analysis of Structures by Concepts of Symmetry and Regularity Book PDF

Author : Ali Kaveh
Publisher : Springer Science & Business Media
Page : 473 pages
File Size : 52,9 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.

Statistics For Dummies

Deborah J. Rumsey
Statistics For Dummies Book PDF

Author : Deborah J. Rumsey
Publisher : John Wiley & Sons
Page : 423 pages
File Size : 41,7 Mb
Release : 2016-06-07
Category : Mathematics
ISBN : 9781119293521

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Statistics For Dummies by Deborah J. Rumsey Pdf

The fun and easy way to get down to business with statistics Stymied by statistics? No fear? this friendly guide offers clear, practical explanations of statistical ideas, techniques, formulas, and calculations, with lots of examples that show you how these concepts apply to your everyday life. Statistics For Dummies shows you how to interpret and critique graphs and charts, determine the odds with probability, guesstimate with confidence using confidence intervals, set up and carry out a hypothesis test, compute statistical formulas, and more. Tracks to a typical first semester statistics course Updated examples resonate with today's students Explanations mirror teaching methods and classroom protocol Packed with practical advice and real-world problems, Statistics For Dummies gives you everything you need to analyze and interpret data for improved classroom or on-the-job performance.