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Author : Xiangwen Li
Publisher :
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4.:/5 (813 download)
Download or read book L(2,1)-labeling of Cubic Cayley Graphs on Dihedral Group written by Xiangwen Li and published by . This book was released on 2007 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On 2-arc-transitive Cayley graphs of dihedral groups written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Azhvan Ahmady
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (926 download)
Download or read book Integral Cayley Graphs written by Azhvan Ahmady and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graph X is said to be integral if all eigenvalues of the adjacency matrix of X are integers. This property was first defined by Harary and Schwenk who suggested the problem of classifying integral graphs. Since the general problem of classifying integral graphs seemed too difficult, graph theorists started to investigate special classes of graphs which included trees, graphs of bounded degree, regular graphs and Cayley graphs. What proves so interesting about this problem is that no one can yet identify what the integral trees are or which 5-regular graphs are integral. In this thesis, integral Cayley graphs are studied. Several topics on the integral Cayley graphs are presented. First, a classification of integral Cayley graphs over abelian groups in terms of the associated Boolean algebra of the subgroups is presented. Secondly, the notions of character and representation integrality are introduced. It has been shown that character integrality is a weaker notion than representation integrality. An internal classification of character integral subsets is proved. General results about representation integral subsets are presented and in an attempt to generalize the results from abelian to non-abelian case, Hamiltonian and dihedral groups are studied. Thirdly, two open problems about integrality of Cayley graphs are solved. Simple eigenvalues in Cayley graphs are studied, and some observations lead to two interesting results in this topic. Finally, the classification of cubic and 4-regular integral Cayley graphs are presented. A general approach to characterize all integral Cayley graphs over abelian groups is presented. Furthermore, a sharp upper bound over the size of the group in terms of the graph degree has been suggested and proved. The thesis concludes with a section devoted to open problems and conjectures in this area.
Author : Štefko Miklavič
Publisher :
ISBN 13 :
Total Pages : 27 pages
Book Rating : 4.:/5 (162 download)
Download or read book Distance-regular Cayley Graphs on Dihedral Groups written by Štefko Miklavič and published by . This book was released on 2005 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Agelos Georgakopoulos
Publisher : American Mathematical Soc.
ISBN 13 : 1470426447
Total Pages : 94 pages
Book Rating : 4.4/5 (74 download)
Download or read book The Planar Cubic Cayley Graphs written by Agelos Georgakopoulos and published by American Mathematical Soc.. This book was released on 2018-01-16 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author obtains a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. He obtains counterexamples to conjectures of Mohar, Bonnington and Watkins. The author's analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.
Author : Jane Marie Young Loftus
Publisher :
ISBN 13 :
Total Pages : 44 pages
Book Rating : 4.:/5 (779 download)
Download or read book Random Walks on Cayley Graphs of Dihedral Groups written by Jane Marie Young Loftus and published by . This book was released on 1999 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 392 pages
Book Rating : 4.3/5 (91 download)
Download or read book Graph Theory Notes of New York written by and published by . This book was released on 1996 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David Joyner
Publisher : JHU Press
ISBN 13 : 0801890136
Total Pages : 329 pages
Book Rating : 4.8/5 (18 download)
Download or read book Adventures in Group Theory written by David Joyner and published by JHU Press. This book was released on 2008-12-29 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: David Joyner uses mathematical toys such as the Rubik's Cube to make abstract algebra and group theory fun. This updated second edition uses SAGE, an open-source computer algebra system, to illustrate many of the computations.
Author : Charles C Pinter
Publisher : Courier Corporation
ISBN 13 : 0486474178
Total Pages : 402 pages
Book Rating : 4.4/5 (864 download)
Download or read book A Book of Abstract Algebra written by Charles C Pinter and published by Courier Corporation. This book was released on 2010-01-14 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
Author : Richard Hammack
Publisher : CRC Press
ISBN 13 : 1439813051
Total Pages : 537 pages
Book Rating : 4.4/5 (398 download)
Download or read book Handbook of Product Graphs written by Richard Hammack and published by CRC Press. This book was released on 2011-06-06 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook examines the dichotomy between the structure of products and their subgraphs. It also features the design of efficient algorithms that recognize products and their subgraphs and explores the relationship between graph parameters of the product and factors. Extensively revised and expanded, this second edition presents full proofs of many important results as well as up-to-date research and conjectures. It illustrates applications of graph products in several areas and contains well over 300 exercises. Supplementary material is available on the book's website.
Author : Dragan Stevanovic
Publisher : Academic Press
ISBN 13 : 0128020970
Total Pages : 167 pages
Book Rating : 4.1/5 (28 download)
Download or read book Spectral Radius of Graphs written by Dragan Stevanovic and published by Academic Press. This book was released on 2014-10-13 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral Radius of Graphs provides a thorough overview of important results on the spectral radius of adjacency matrix of graphs that have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author. The primer begins with a brief classical review, in order to provide the reader with a foundation for the subsequent chapters. Topics covered include spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem. From this introduction, the book delves deeper into the properties of the principal eigenvector; a critical subject as many of the results on the spectral radius of graphs rely on the properties of the principal eigenvector for their proofs. A following chapter surveys spectral radius of special graphs, covering multipartite graphs, non-regular graphs, planar graphs, threshold graphs, and others. Finally, the work explores results on the structure of graphs having extreme spectral radius in classes of graphs defined by fixing the value of a particular, integer-valued graph invariant, such as: the diameter, the radius, the domination number, the matching number, the clique number, the independence number, the chromatic number or the sequence of vertex degrees. Throughout, the text includes the valuable addition of proofs to accompany the majority of presented results. This enables the reader to learn tricks of the trade and easily see if some of the techniques apply to a current research problem, without having to spend time on searching for the original articles. The book also contains a handful of open problems on the topic that might provide initiative for the reader's research. - Dedicated coverage to one of the most prominent graph eigenvalues - Proofs and open problems included for further study - Overview of classical topics such as spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem
Author : R.L. Graham
Publisher : Elsevier
ISBN 13 : 044488002X
Total Pages : 1283 pages
Book Rating : 4.4/5 (448 download)
Download or read book Handbook of Combinatorics written by R.L. Graham and published by Elsevier. This book was released on 1995-12-11 with total page 1283 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : W. David Joyner
Publisher : Birkhäuser
ISBN 13 : 3319683837
Total Pages : 344 pages
Book Rating : 4.3/5 (196 download)
Download or read book Adventures in Graph Theory written by W. David Joyner and published by Birkhäuser. This book was released on 2017-12-28 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook acts as a pathway to higher mathematics by seeking and illuminating the connections between graph theory and diverse fields of mathematics, such as calculus on manifolds, group theory, algebraic curves, Fourier analysis, cryptography and other areas of combinatorics. An overview of graph theory definitions and polynomial invariants for graphs prepares the reader for the subsequent dive into the applications of graph theory. To pique the reader’s interest in areas of possible exploration, recent results in mathematics appear throughout the book, accompanied with examples of related graphs, how they arise, and what their valuable uses are. The consequences of graph theory covered by the authors are complicated and far-reaching, so topics are always exhibited in a user-friendly manner with copious graphs, exercises, and Sage code for the computation of equations. Samples of the book’s source code can be found at github.com/springer-math/adventures-in-graph-theory. The text is geared towards advanced undergraduate and graduate students and is particularly useful for those trying to decide what type of problem to tackle for their dissertation. This book can also serve as a reference for anyone interested in exploring how they can apply graph theory to other parts of mathematics.
Author : Steven Skiena
Publisher : Addison-Wesley Longman
ISBN 13 : 9780201694673
Total Pages : 344 pages
Book Rating : 4.6/5 (946 download)
Download or read book Implementing Discrete Mathematics written by Steven Skiena and published by Addison-Wesley Longman. This book was released on 1996 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concentrates on two distinct areas in discrete mathematics. The first section deals with combinatorics, loosely defined as the study of counting. We provide functions for generating combinatorial objects such as permutations, partitions, and Young tableaux, as well as for studying various aspects of these structures.The second section considers graph theory, which can be defined equally loosely as the study of binary relations. We consider a wide variety of graphs, provide functions to create them, and functions to show what special properties they have, Although graphs are combinatorial structures, understanding them requires pictures or embeddings. Thus we provide functions to create a variety of graph embeddings, so the same structure can be viewed in several different ways. Algorithmic graph theory is an important interface between mathematics and computer science, and so we study a variety of polynominal and exponential time problems.
Author : Tomaz Pisanski
Publisher : Springer Science & Business Media
ISBN 13 : 0817683631
Total Pages : 289 pages
Book Rating : 4.8/5 (176 download)
Download or read book Configurations from a Graphical Viewpoint written by Tomaz Pisanski and published by Springer Science & Business Media. This book was released on 2013 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Configurations can be studied from a graph-theoretical viewpoint via the so-called Levi graphs and lie at the heart of graphs, groups, surfaces, and geometries, all of which are very active areas of mathematical exploration. In this self-contained textbook, algebraic graph theory is used to introduce groups; topological graph theory is used to explore surfaces; and geometric graph theory is implemented to analyze incidence geometries. After a preview of configurations in Chapter 1, a concise introduction to graph theory is presented in Chapter 2, followed by a geometric introduction to groups in Chapter 3. Maps and surfaces are combinatorially treated in Chapter 4. Chapter 5 introduces the concept of incidence structure through vertex colored graphs, and the combinatorial aspects of classical configurations are studied. Geometric aspects, some historical remarks, references, and applications of classical configurations appear in the last chapter. With over two hundred illustrations, challenging exercises at the end of each chapter, a comprehensive bibliography, and a set of open problems, Configurations from a Graphical Viewpoint is well suited for a graduate graph theory course, an advanced undergraduate seminar, or a self-contained reference for mathematicians and researchers.
Author : Gordon James
Publisher : Cambridge University Press
ISBN 13 : 1139811053
Total Pages : 436 pages
Book Rating : 4.1/5 (398 download)
Download or read book Representations and Characters of Groups written by Gordon James and published by Cambridge University Press. This book was released on 2001-10-18 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a modern introduction to the representation theory of finite groups. Now in its second edition, the authors have revised the text and added much new material. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. Included here are the character tables of all groups of order less than 32, and all simple groups of order less than 1000. Applications covered include Burnside's paqb theorem, the use of character theory in studying subgroup structure and permutation groups, and how to use representation theory to investigate molecular vibration. Each chapter features a variety of exercises, with full solutions provided at the end of the book. This will be ideal as a course text in representation theory, and in view of the applications, will be of interest to chemists and physicists as well as mathematicians.
Author : Cornelia Druţu
Publisher : American Mathematical Soc.
ISBN 13 : 1470411040
Total Pages : 841 pages
Book Rating : 4.4/5 (74 download)
Download or read book Geometric Group Theory written by Cornelia Druţu and published by American Mathematical Soc.. This book was released on 2018-03-28 with total page 841 pages. Available in PDF, EPUB and Kindle. Book excerpt: The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's Property (T) and the Haagerup property, as well as their characterizations in terms of group actions on median spaces and spaces with walls. The book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the first book in which geometric group theory is presented in a form accessible to advanced graduate students and young research mathematicians. It fills a big gap in the literature and will be used by researchers in geometric group theory and its applications.
