Foundations of topological graph theory, Bonnington, C. Paul Little, Charles H. C.
Àâòîð: Godsil Chris, Royle Gordon F. Íàçâàíèå: Algebraic Graph Theory ISBN: 0387952411 ISBN-13(EAN): 9780387952413 Èçäàòåëüñòâî: Springer Ðåéòèíã: Öåíà: 11313.00 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.
Îïèñàíèå: Algebraic graph theory is a combination of two strands. The first is the study of algebraic objects associated with graphs. The second is the use of tools from algebra to derive properties of graphs. This work illustrates the main tools and ideas of algebraic graph theory.
Îïèñàíèå: This undergraduate textbook provides an introduction to graph theory, which has numerous applications in modeling problems in science and technology, and has become a vital component to computer science, computer science and engineering, and mathematics curricula of universities all over the world. The author follows a methodical and easy to understand approach. Beginning with the historical background, motivation and applications of graph theory, the author first explains basic graph theoretic terminologies.
From this firm foundation, the author goes on to present paths, cycles, connectivity, trees, matchings, coverings, planar graphs, graph coloring and digraphs as well as some special classes of graphs together with some research topics for advanced study. Filled with exercises and illustrations, Basic Graph Theory is a valuable resource for any undergraduate student to understand and gain confidence in graph theory and its applications to scientific research, algorithms and problem solving.
Àâòîð: W. T. Tutte Íàçâàíèå: Graph theory ISBN: 0521794897 ISBN-13(EAN): 9780521794893 Èçäàòåëüñòâî: Cambridge Academ Ðåéòèíã: Öåíà: 8078.00 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.
Îïèñàíèå: Designed for non-specialists, this classic text by a world expert is an invaluable reference for those seeking a basic understanding of the subject. Exercises, notes and exhaustive references follow each chapter, making it outstanding both as a text and reference for students and researchers in graph theory and its applications.
Îïèñàíèå: ‘Network’ is a heavily overloaded term, so that ‘network analysis’ means different things to different people. Specific forms of network analysis are used in the study of diverse structures such as the Internet, interlocking directorates, transportation systems, epidemic spreading, metabolic pathways, the Web graph, electrical circuits, project plans, and so on. There is, however, a broad methodological foundation which is quickly becoming a prerequisite for researchers and practitioners working with network models.From a computer science perspective, network analysis is applied graph theory. Unlike standard graph theory books, the content of this book is organized according to methods for specific levels of analysis (element, group, network) rather than abstract concepts like paths, matchings, or spanning subgraphs. Its topics therefore range from vertex centrality to graph clustering and the evolution of scale-free networks.In 15 coherent chapters, this monograph-like tutorial book introduces and surveys the concepts and methods that drive network analysis, and is thus the first book to do so from a methodological perspective independent of specific application areas.
Îïèñàíèå: A number of important results in combinatorics, discrete geometry, and theoretical computer science have been proved using algebraic topology. While the results are quite famous, their proofs are not so widely understood. They are scattered in research papers or outlined in surveys, and they often use topological notions not commonly known among combinatorialists or computer scientists.This book is the first textbook treatment of a significant part of such results. It focuses on so-called equivariant methods, based on the Borsuk-Ulam theorem and its generalizations. The topological tools are intentionally kept on a very elementary level (for example, homology theory and homotopy groups are completely avoided). No prior knowledge of algebraic topology is assumed, only a background in undergraduate mathematics, and the required topological notions and results are gradually explained. This text started with a one-semester graduate course the author taught in fall 1993 in Prague. The transcripts of the lectures by the participants served as a basis of the first version. Some years later, a course partially based on that text was taught by Günter M. Ziegler in Berlin. The book is based on a thoroughly rewritten version prepared during a pre-doctoral course the author taught at the ETH Zurich in fall 2001.Most of the material was covered in the course: Chapter 1 was assigned as an introductory reading text, and the other chapters were presented in approximately 30 hours of teaching (by 45 minutes), with some omissions throughout and with only a sketchy presentation of the last chapter.
Àâòîð: Godsil Chris, Royle Gordon Íàçâàíèå: Algebraic graph theory ISBN: 0387952209 ISBN-13(EAN): 9780387952208 Èçäàòåëüñòâî: Springer Ðåéòèíã: Öåíà: 5583.00 ð. Íàëè÷èå íà ñêëàäå: Åñòü ó ïîñòàâùèêà Ïîñòàâêà ïîä çàêàç.
Îïèñàíèå: This book is primarily aimed at graduate students and researchers in graph theory, combinatorics, or discrete mathematics in general. However, all the necessary graph theory is developed from scratch, so the only pre-requisite for reading it is a first course in linear algebra and a small amount of elementary group theory. It should be accessible to motivated upper-level undergraduates.
