Isomorphisms Symmetry And Computations In Algebraic Graph Theory

Author : Gareth A. Jones,Ilia Ponomarenko,Jozef Širáň
Publisher : Springer Nature
Page : 234 pages
File Size : 50,6 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 : Lowell W. Beineke,Robin J. Wilson,Peter J. Cameron
Publisher : Cambridge University Press
Page : 128 pages
File Size : 42,8 Mb
Release : 2004-10-04
Category : Mathematics
ISBN : 9781107079458

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

The rapidly expanding area of algebraic graph theory uses two different branches of algebra to explore various aspects of graph theory: linear algebra (for spectral theory) and group theory (for studying graph symmetry). These areas have links with other areas of mathematics, such as logic and harmonic analysis, and are increasingly being used in such areas as computer networks where symmetry is an important feature. Other books cover portions of this material, but this book is unusual in covering both of these aspects and there are no other books with such a wide scope. Peter J. Cameron, internationally recognized for his substantial contributions to the area, served as academic consultant for this volume, and the result is ten expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory, linear algebra and group theory. Each chapter concludes with an extensive list of references.

Author : Edward Tauscher Dobson,Aleksander Malnič,Dragan Marušič
Publisher : Unknown
Page : 128 pages
File Size : 50,8 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"--

Author : Ashay Dharwadker,John-Tagore Tevet
Publisher : Institute of Mathematics
Page : 42 pages
File Size : 51,9 Mb
Release : 2009-08-08
Category : Mathematics
ISBN : 9781466394377

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The Graph Isomorphism Algorithm by Ashay Dharwadker,John-Tagore Tevet Pdf

We present a new polynomial-time algorithm for determining whether two given graphs are isomorphic or not. We prove that the algorithm is necessary and sufficient for solving the Graph Isomorphism Problem in polynomial-time, thus showing that the Graph Isomorphism Problem is in P. The semiotic theory for the recognition of graph structure is used to define a canonical form of the sign matrix of a graph. We prove that the canonical form of the sign matrix is uniquely identifiable in polynomial-time for isomorphic graphs. The algorithm is demonstrated by solving the Graph Isomorphism Problem for many of the hardest known examples. We implement the algorithm in C++ and provide a demonstration program for Microsoft Windows.

Author : Christoph Martin Hoffmann
Publisher : Springer
Page : 328 pages
File Size : 49,7 Mb
Release : 1982
Category : Mathematics
ISBN : UOM:39015002059098

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Group-theoretic Algorithms and Graph Isomorphism by Christoph Martin Hoffmann Pdf

Author : Andries E. Brouwer,H. Van Maldeghem
Publisher : Unknown
Page : 481 pages
File Size : 50,9 Mb
Release : 2022-01-13
Category : Language Arts & Disciplines
ISBN : 9781316512036

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Strongly Regular Graphs by Andries E. Brouwer,H. Van Maldeghem Pdf

This monograph on strongly regular graphs is an invaluable reference for anybody working in algebraic combinatorics.

Author : Shio Gai Quek,Said Broumi,Ganeshsree Selvachandran,Assia Bakali,Mohamed Talea,Florentin Smarandache
Publisher : Infinite Study
Page : 32 pages
File Size : 44,8 Mb
Release : 2024-05-20
Category : Mathematics
ISBN : 8210379456XXX

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Some Results on the Graph Theory for Complex Neutrosophic Sets by Shio Gai Quek,Said Broumi,Ganeshsree Selvachandran,Assia Bakali,Mohamed Talea,Florentin Smarandache Pdf

Fuzzy graph theory plays an important role in the study of the symmetry and asymmetry properties of fuzzy graphs.

Author : Josef Lauri,Raffaele Scapellato
Publisher : Cambridge University Press
Page : 207 pages
File Size : 53,9 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.

Author : László Lovász,Vera T. Sós
Publisher : Unknown
Page : 412 pages
File Size : 41,7 Mb
Release : 1981
Category : Algebra
ISBN : UCSD:31822001199058

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Algebraic Methods in Graph Theory by László Lovász,Vera T. Sós Pdf

Author : Christopher H Griffin
Publisher : World Scientific
Page : 305 pages
File Size : 40,8 Mb
Release : 2023-08-08
Category : Mathematics
ISBN : 9789811273124

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Applied Graph Theory: An Introduction With Graph Optimization And Algebraic Graph Theory by Christopher H Griffin Pdf

This book serves as an introduction to graph theory and its applications. It is intended for a senior undergraduate course in graph theory but is also appropriate for beginning graduate students in science or engineering. The book presents a rigorous (proof-based) introduction to graph theory while also discussing applications of the results for solving real-world problems of interest. The book is divided into four parts. Part 1 covers the combinatorial aspects of graph theory including a discussion of common vocabulary, a discussion of vertex and edge cuts, Eulerian tours, Hamiltonian paths and a characterization of trees. This leads to Part 2, which discusses common combinatorial optimization problems. Spanning trees, shortest path problems and matroids are all discussed, as are maximum flow problems. Part 2 ends with a discussion of graph coloring and a proof of the NP-completeness of the coloring problem. Part 3 introduces the reader to algebraic graph theory, and focuses on Markov chains, centrality computation (e.g., eigenvector centrality and page rank), as well as spectral graph clustering and the graph Laplacian. Part 4 contains additional material on linear programming, which is used to provide an alternative analysis of the maximum flow problem. Two appendices containing prerequisite material on linear algebra and probability theory are also provided.

Author : Damien Calaque,Carlo Antonio Rossi
Publisher : European Mathematical Society
Page : 120 pages
File Size : 52,5 Mb
Release : 2011
Category : Cohomology operations
ISBN : 3037190965

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Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry by Damien Calaque,Carlo Antonio Rossi Pdf

The Duflo isomorphism first appeared in Lie theory and representation theory. It is an isomorphism between invariant polynomials of a Lie algebra and the center of its universal enveloping algebra, generalizing the pioneering work of Harish-Chandra on semi-simple Lie algebras. Kontsevich later refined Duflo's result in the framework of deformation quantization and also observed that there is a similar isomorphism between Dolbeault cohomology of holomorphic polyvector fields on a complex manifold and its Hochschild cohomology. This book, which arose from a series of lectures by Damien Calaque at ETH, derives these two isomorphisms from a Duflo-type result for $Q$-manifolds. All notions mentioned above are introduced and explained in this book. The only prerequisites are basic linear algebra and differential geometry. In addition to standard notions such as Lie (super) algebras, complex manifolds, Hochschild and Chevalley-Eilenberg cohomologies, spectral sequences, Atiyah and Todd classes, the graphical calculus introduced by Kontsevich in his seminal work on deformation quantization is addressed in detail. This book is well suited for graduate students in mathematics and mathematical physics as well as researchers working in Lie theory, algebraic geometry, and deformation theory.

Author : Ted Dobson,Aleksander Malnič,Dragan Marušič
Publisher : Cambridge University Press
Page : 527 pages
File Size : 53,6 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.

Author : Chris Godsil,Gordon F. Royle
Publisher : Springer Science & Business Media
Page : 453 pages
File Size : 43,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461301639

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Algebraic Graph Theory by Chris Godsil,Gordon F. Royle Pdf

This book presents and illustrates the main tools and ideas of algebraic graph theory, with a primary emphasis on current rather than classical topics. It is designed to offer self-contained treatment of the topic, with strong emphasis on concrete examples.

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 564 pages
File Size : 44,7 Mb
Release : 2007-11-23
Category : Mathematics
ISBN : 9780306483738

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Encyclopaedia of Mathematics, Supplement III by Michiel Hazewinkel Pdf

This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.

Author : Gena Hahn,Gert Sabidussi
Publisher : Springer Science & Business Media
Page : 456 pages
File Size : 46,7 Mb
Release : 1997-06-30
Category : Mathematics
ISBN : 0792346688

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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.