Spectral Radius Of Graphs

Paperback | September 24, 2014

byDragan StevanovicEditorDragan Stevanovic

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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have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author.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

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From the Publisher

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 ...

From the Jacket

Spectral Radius of Graphsprovides 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 o...

Format:PaperbackDimensions:166 pages, 8.75 × 6.35 × 0.68 inPublished:September 24, 2014Publisher:Academic PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0128020687

ISBN - 13:9780128020685

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Table of Contents

Chapter 1: Introduction Chapter 2: Properties of the principal eigenvector Chapter 3: Spectral radius of special graphs Chapter 4: Extremal graphs for the spectral radius

Editorial Reviews

"It covers topics of great interest which are attractive not only to researchers in graph theory, but also to other specialists. Therefore, especially for a researcher in the field, this monograph is a must-buy!"--Zentralblatt MATH, Spectral Radius of Graphs