Symmetry In Graph Theory

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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 : 41,5 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

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 : 40,8 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.

Symmetry in Graph Theory

Jose M. Rodriguez
Symmetry in Graph Theory Book PDF

Author : Jose M. Rodriguez
Publisher : MDPI
Page : 340 pages
File Size : 40,6 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 : 51,9 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 : 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.

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 : 43,9 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.

Algebraic Graph Theory

Norman Biggs
Algebraic Graph Theory Book PDF

Author : Norman Biggs
Publisher : Cambridge University Press
Page : 220 pages
File Size : 47,6 Mb
Release : 1993
Category : Mathematics
ISBN : 0521458978

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Algebraic Graph Theory by Norman Biggs Pdf

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.

Symmetry

István Hargittai
Symmetry Book PDF

Author : István Hargittai
Publisher : Elsevier
Page : 1068 pages
File Size : 43,7 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.

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 : 49,7 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.

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 : 42,7 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.

Topics in Algebraic Graph Theory

Lowell W. Beineke,Robin J. Wilson
Topics in Algebraic Graph Theory Book PDF

Author : Lowell W. Beineke,Robin J. Wilson
Publisher : Cambridge University Press
Page : 302 pages
File Size : 42,8 Mb
Release : 2004-10-04
Category : Mathematics
ISBN : 0521801974

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Topics in Algebraic Graph Theory by Lowell W. Beineke,Robin J. Wilson Pdf

There is no other book with such a wide scope of both areas of algebraic graph theory.

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 : 50,7 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.

Spectral Graph Theory

Fan R. K. Chung
Spectral Graph Theory Book PDF

Author : Fan R. K. Chung
Publisher : American Mathematical Soc.
Page : 228 pages
File Size : 50,9 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 0821889362

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Spectral Graph Theory by Fan R. K. Chung Pdf

Beautifully written and elegantly presented, this book is based on 10 lectures given at the CBMS workshop on spectral graph theory in June 1994 at Fresno State University. Chung's well-written exposition can be likened to a conversation with a good teacher - one who not only gives you the facts, but tells you what is really going on, why it is worth doing, and how it is related to familiar ideas in other areas. The monograph is accessible to the nonexpert who is interested in reading about this evolving area of mathematics.

Graph Theory (on Demand Printing Of 02787)

Frank Harary
Graph Theory on Demand Printing Of 02787 Book PDF

Author : Frank Harary
Publisher : CRC Press
Page : 288 pages
File Size : 47,8 Mb
Release : 2018-03-05
Category : Mathematics
ISBN : 9780429962318

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Graph Theory (on Demand Printing Of 02787) by Frank Harary Pdf

An effort has been made to present the various topics in the theory of graphs in a logical order, to indicate the historical background, and to clarify the exposition by including figures to illustrate concepts and results. In addition, there are three appendices which provide diagrams of graphs, directed graphs, and trees. The emphasis throughout is on theorems rather than algorithms or applications, which however are occaisionally mentioned.

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 : 55,8 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.