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Author : R. Balakrishnan
ISBN : 9781461445289
Genre : Mathematics
File Size : 20.24 MB
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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.

Author : R. Balakrishnan
ISBN : 9781461445296
Genre : Mathematics
File Size : 24.14 MB
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This second edition includes two new chapters: one on domination in graphs and the other on the spectral properties of graphs, the latter including a discussion on graph energy. The chapter on graph colorings has been enlarged, covering additional topics such as homomorphisms and colorings and the uniqueness of the Mycielskian up to isomorphism. This book also introduces several interesting topics such as Dirac's theorem on k-connected graphs, Harary-Nashwilliam's theorem on the hamiltonicity of line graphs, Toida-McKee's characterization of Eulerian graphs, the Tutte matrix of a graph, Fournier's proof of Kuratowski's theorem on planar graphs, the proof of the nonhamiltonicity of the Tutte graph on 46 vertices, and a concrete application of triangulated graphs.

Author : R. Balakrishnan
ISBN : 0387988599
Genre : Mathematics
File Size : 68.18 MB
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Here is a solid introduction to graph theory, covering Dirac's theorem on k-connected graphs, Harary-Nashwilliam's theorem on the hamiltonicity of line graphs, Toida-McKee's characterization of Eulerian graphs, Fournier's proof of Kuratowski's theorem on planar graphs, and more. The book does not presuppose deep knowledge of any branch of mathematics, but requires only the basics of mathematics.

In the spectrum of mathematics, graph theory which studies a mathe matical structure on a set of elements with a binary relation, as a recognized discipline, is a relative newcomer. In recent three decades the exciting and rapidly growing area of the subject abounds with new mathematical devel opments and significant applications to real-world problems. More and more colleges and universities have made it a required course for the senior or the beginning postgraduate students who are majoring in mathematics, computer science, electronics, scientific management and others. This book provides an introduction to graph theory for these students. The richness of theory and the wideness of applications make it impossi ble to include all topics in graph theory in a textbook for one semester. All materials presented in this book, however, I believe, are the most classical, fundamental, interesting and important. The method we deal with the mate rials is to particularly lay stress on digraphs, regarding undirected graphs as their special cases. My own experience from teaching out of the subject more than ten years at University of Science and Technology of China (USTC) shows that this treatment makes hardly the course di:fficult, but much more accords with the essence and the development trend of the subject.

Author : Richard J. Trudeau
ISBN : 9780486318660
Genre : Mathematics
File Size : 88.81 MB
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Aimed at "the mathematically traumatized," this text offers nontechnical coverage of graph theory, with exercises. Discusses planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. 1976 edition.

Author : Daniel Marcus
ISBN : 0883857537
Genre : Mathematics
File Size : 42.69 MB
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Combining the features of a textbook with those of a problem workbook, this text for mathematics, computer science and engineering students presents a natural, friendly way to learn some of the essential ideas of graph theory. The material is explained using 360 strategically placed problems with connecting text, which is then supplemented by 280 additional homework problems. This problem-oriented format encourages active involvement by the reader while always giving clear direction. This approach is especially valuable with the presentation of proofs, which become more frequent and elaborate as the book progresses. Arguments are arranged in digestible chunks and always appear together with concrete examples to help remind the reader of the bigger picture. Topics include spanning tree algorithms, Euler paths, Hamilton paths and cycles, independence and covering, connections and obstructions, and vertex and edge colourings.

Author : Gary Chartrand
ISBN : 9780486297309
Genre : Mathematics
File Size : 25.99 MB
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Written by two prominent figures in the field, this comprehensive text provides a remarkably student-friendly approach. Its sound yet accessible treatment emphasizes the history of graph theory and offers unique examples and lucid proofs. 2004 edition.

The first part of this text covers the main graph theoretic topics: connectivity, trees, traversability, planarity, colouring, covering, matching, digraphs, networks, matrices of a graph, graph theoretic algorithms, and matroids. These concepts are then applied in the second part to problems in engineering, operations research, and science as well as to an interesting set of miscellaneous problems, thus illustrating their broad applicability. Every effort has been made to present applications that use not merely the notation and terminology of graph theory, but also its actual mathematical results. Some of the applications, such as in molecular evolution, facilities layout, and graffic network design, have never appeared before in book form. Written at an advanced undergraduate to beginning graduate level, this book is suitable for students of mathematics, engineering, operations research, computer science, and physical sciences as well as for researchers and practitioners with an interest in graph theoretic modelling.

Author : Dieter Jungnickel
ISBN : 9783642322785
Genre : Mathematics
File Size : 78.29 MB
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From the reviews of the previous editions ".... The book is a first class textbook and seems to be indispensable for everybody who has to teach combinatorial optimization. It is very helpful for students, teachers, and researchers in this area. The author finds a striking synthesis of nice and interesting mathematical results and practical applications. ... the author pays much attention to the inclusion of well-chosen exercises. The reader does not remain helpless; solutions or at least hints are given in the appendix. Except for some small basic mathematical and algorithmic knowledge the book is self-contained. ..." K.Engel, Mathematical Reviews 2002 The substantial development effort of this text, involving multiple editions and trailing in the context of various workshops, university courses and seminar series, clearly shows through in this new edition with its clear writing, good organisation, comprehensive coverage of essential theory, and well-chosen applications. The proofs of important results and the representation of key algorithms in a Pascal-like notation allow this book to be used in a high-level undergraduate or low-level graduate course on graph theory, combinatorial optimization or computer science algorithms. The well-worked solutions to exercises are a real bonus for self study by students. The book is highly recommended. P .B. Gibbons, Zentralblatt für Mathematik 2005 Once again, the new edition has been thoroughly revised. In particular, some further material has been added: more on NP-completeness (especially on dominating sets), a section on the Gallai-Edmonds structure theory for matchings, and about a dozen additional exercises – as always, with solutions. Moreover, the section on the 1-factor theorem has been completely rewritten: it now presents a short direct proof for the more general Berge-Tutte formula. Several recent research developments are discussed and quite a few references have been added.

Author : Jonathan L. Gross
ISBN : 9781584885054
Genre : Mathematics
File Size : 87.10 MB
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Already an international bestseller, with the release of this greatly enhanced second edition, Graph Theory and Its Applications is now an even better choice as a textbook for a variety of courses -- a textbook that will continue to serve your students as a reference for years to come. The superior explanations, broad coverage, and abundance of illustrations and exercises that positioned this as the premier graph theory text remain, but are now augmented by a broad range of improvements. Nearly 200 pages have been added for this edition, including nine new sections and hundreds of new exercises, mostly non-routine. What else is new? New chapters on measurement and analytic graph theory Supplementary exercises in each chapter - ideal for reinforcing, reviewing, and testing. Solutions and hints, often illustrated with figures, to selected exercises - nearly 50 pages worth Reorganization and extensive revisions in more than half of the existing chapters for smoother flow of the exposition Foreshadowing - the first three chapters now preview a number of concepts, mostly via the exercises, to pique the interest of reader Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.