This graduate level text is distinguished both by the range of topics and the novelty of the material it treats--more than half of the material in it has previously only appeared in research papers. The first half of this book introduces the characteristic and matchings polynomials of a graph. It is instructive to consider these polynomials together because they have a number of properties in common. The matchings polynomial has links with a number of problems in combinatorial enumeration, particularly some of the current work on the combinatorics of orthogonal polynomials. This connection is discussed at some length, and is also in part the stimulus for the inclusion of chapters on orthogonal polynomials and formal power series. Many of the properties of orthogonal polynomials are derived from properties of characteristic polynomials. The second half of the book introduces the theory of polynomial spaces, which provide easy access to a number of important results in design theory, coding theory and the theory of association schemes. This book should be of interest to second year graduate text/reference in mathematics.
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The topics have been thoughtfully chosen and masterfully integrated into the text. The result is a delightfully entertaining and informative excursion into the field...this text provides the most comprehensive treatment I have encountered...this book is likely to become a permanent fixture in the study...
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First Sentence:
Let G be a graph with n vertices. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Discrete Math, Graph Theory, Academic Press, London Math, Philips Research Reports Supplements, Lecture Notes, Linear Algebra Appl, Eindhoven University of Technology, American Math, Cambridge University Press, Matching Theory, Pure Math New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Let G be a graph with n vertices. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Discrete Math, Graph Theory, Academic Press, London Math, Philips Research Reports Supplements, Lecture Notes, Linear Algebra Appl, Eindhoven University of Technology, American Math, Cambridge University Press, Matching Theory, Pure Math New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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This book cites 27
books:
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- Algebraic Graph Theory (Cambridge Mathematical Library) by Norman Biggs on page 36, page 92, and page 218
- An Introduction to Orthogonal Polynomials (Mathematics and Its Applications) by T. S. Chihara on page 147, and page 175
- Special Functions (Encyclopedia of Mathematics and its Applications) by George E. Andrews on page 147, and page 175
- Recent Results in the Theory of Graph Spectra (Annals of Discrete Mathematics) by Dragos M. Cvetkovic on page 18, and page 36
- Local Fields (London Mathematical Society Student Texts) by J. W. S. Cassels on page 50
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