Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 804 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
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.
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.
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have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author.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
Download or read book A Textbook of Graph Theory written by R. Balakrishnan and published by Springer Science & Business Media. This book was released on 2012-09-20 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: In its second edition, expanded with new chapters on domination in graphs and on the spectral properties of graphs, this book offers a solid background in the basics of graph theory. Introduces such topics as Dirac's theorem on k-connected graphs and more.
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.
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.
Download or read book Graphical Enumeration written by Frank Harary and published by Elsevier. This book was released on 2014-05-10 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graphical Enumeration deals with the enumeration of various kinds of graphs. Topics covered range from labeled enumeration and George Pólya's theorem to rooted and unrooted trees, graphs and digraphs, and power group enumeration. Superposition, blocks, and asymptotics are also discussed. A number of unsolved enumeration problems are presented. Comprised of 10 chapters, this book begins with an overview of labeled graphs, followed by a description of the basic enumeration theorem of Pólya. The next three chapters count an enormous variety of trees, graphs, and digraphs. The Power Group Enumeration Theorem is then described together with some of its applications, including the enumeration of self-complementary graphs and digraphs and finite automata. Two other chapters focus on the counting of superposition and blocks, while another chapter is devoted to asymptotic numbers that are developed for several different graphical structures. The book concludes with a comprehensive definitive list of unsolved graphical enumeration problems. This monograph will be of interest to both students and practitioners of mathematics.
Download or read book Connectivity in Graphs written by W. T. Tutte and published by . This book was released on 1966 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modern Algebra Abstract Algebra written by and published by Krishna Prakashan Media. This book was released on with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Regular Subgroups of Primitive Permutation Groups written by Martin W. Liebeck and published by American Mathematical Soc.. This book was released on 2010 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: Addresses the classical problem of determining finite primitive permutation groups G with a regular subgroup B.
Download or read book Graph Theoretical Approaches to Chemical Reactivity written by Danail D. Bonchev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: The progress in computer technology during the last 10-15 years has enabled the performance of ever more precise quantum mechanical calculations related to structure and interactions of chemical compounds. However, the qualitative models relating electronic structure to molecular geometry have not progressed at the same pace. There is a continuing need in chemistry for simple concepts and qualitatively clear pictures that are also quantitatively comparable to ab initio quantum chemical calculations. Topological methods and, more specifically, graph theory as a fixed-point topology, provide in principle a chance to fill this gap. With its more than 100 years of applications to chemistry, graph theory has proven to be of vital importance as the most natural language of chemistry. The explosive development of chemical graph theory during the last 20 years has increasingly overlapped with quantum chemistry. Besides contributing to the solution of various problems in theoretical chemistry, this development indicates that topology is an underlying principle that explains the success of quantum mechanics and goes beyond it, thus promising to bear more fruit in the future.
Download or read book Problems on Mapping Class Groups and Related Topics written by Benson Farb and published by American Mathematical Soc.. This book was released on 2006-09-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.
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.
Download or read book Graphs on Surfaces and Their Applications written by Sergei K. Lando and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs (Grothendieck's theory of "dessins d'enfants"), the matrix integral method, moduli spaces of curves, the topology of meromorphic functions, and combinatorial aspects of Vassiliev's knot invariants and, in an appendix by Don Zagier, the use of finite group representation theory. The presentation is concrete throughout, with numerous figures, examples (including computer calculations) and exercises, and should appeal to both graduate students and researchers.
Download or read book Networks Topology and Dynamics written by Ahmad K. Naimzada and published by Springer Science & Business Media. This book was released on 2008-11-14 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is convergent consensus among scientists that many social, economic and ?nancial phenomena can be described by a network of agents and their inter- tions. Surprisingly, even though the application ?elds are quite different, those n- works often show a common behaviour. Thus, their topological properties can give useful insights on how the network is structured, which are the most “important” nodes/agents, how the network reacts to new arrivals. Moreover the network, once included into a dynamic context, helps to model many phenomena. Among the t- ics in which topology and dynamics are the essential tools, we will focus on the diffusion of technologies and fads, the rise of industrial districts, the evolution of ?nancial markets, cooperation and competition, information ?ows, centrality and prestige. The volume, including recent contributions to the ?eld of network modelling, is based on the communications presented at NET 2006 (Verbania, Italy) and NET 2007 (Urbino, Italy); offers a wide range of recent advances, both theoretical and methodological, that will interest academics as well as practitioners. Theory and applications are nicely integrated: theoretical papers deal with graph theory, game theory, coalitions, dynamics, consumer behavior, segregation models and new contributions to the above mentioned area. The applications cover a wide range: airline transportation, ?nancial markets, work team organization, labour and credit market.
