Spectral Radius of Graphs

Download or Read online Spectral Radius of Graphs full in PDF, ePub and kindle. This book written by Dragan Stevanovic and published by Academic Press which was released on 13 October 2014 with total pages 166. We cannot guarantee that Spectral Radius of Graphs book is available in the library, click Get Book button to download or read online books. Join over 650.000 happy Readers and READ as many books as you like.

Spectral Radius of Graphs
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Publisher : Academic Press
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ISBN : 9780128020975
Pages : 166 pages
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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have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author.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

Spectral Radius of Graphs

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

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The Minimal Spectral Radius of Graphs with a Given Diameter

Download or read online The Minimal Spectral Radius of Graphs with a Given Diameter written by E.R. van Dam,R.E. Kooij, published by Unknown which was released on 2006. Get The Minimal Spectral Radius of Graphs with a Given Diameter Books now! Available in PDF, ePub and Kindle.

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On the Spectral Radius of Graphs with a Given Domination Number

Download or read online On the Spectral Radius of Graphs with a Given Domination Number written by Dragan Stevanović,Pierre Hansen,Mustapha Aouchiche,Groupe d'études et de recherche en analyse des décisions (Montréal, Québec), published by Unknown which was released on 2007. Get On the Spectral Radius

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The Minimum Spectral Radius of Graphs with a Given Clique Number

Download or read online The Minimum Spectral Radius of Graphs with a Given Clique Number written by Dragan Stevanović,Pierre Hansen,Groupe d'études et de recherche en analyse des décisions (Montréal, Québec), published by Unknown which was released on 2007. Get The Minimum Spectral Radius of Graphs

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Asymptotic Results on the Spectral Radius and the Diameter of Graphs

Download or read online Asymptotic Results on the Spectral Radius and the Diameter of Graphs written by Sebastian M. Cioabǎ, published by Unknown which was released on 2008. Get Asymptotic Results on the Spectral Radius and the Diameter of Graphs Books now! Available in PDF, ePub and Kindle.

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Spectral Radius and Signless Laplacian Spectral Radius of K connected Graphs

The adjacency matrix of a graph is a (0, 1)-matrix indexed by the vertex set of the graph. And the signless Laplacian matrix of a graph is the sum of its adjacency matrix and its diagonal matrix of vertex degrees. The eigenvalues and the signless Laplacian eigenvalues of a graph are

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Comparing the Geometric  arithmetic Index and the Spectral Radius of Graphs

Download or read online Comparing the Geometric arithmetic Index and the Spectral Radius of Graphs written by Mustapha Aouchiche, published by Unknown which was released on 2016. Get Comparing the Geometric arithmetic Index and the Spectral Radius of Graphs Books now! Available in PDF, ePub and Kindle.

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Spectra of Graphs

This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics. Exercises at

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Graphs with Given Diameter Maximizing the Spectral Radius

Download or read online Graphs with Given Diameter Maximizing the Spectral Radius written by E.R. van Dam, published by Unknown which was released on 2006. Get Graphs with Given Diameter Maximizing the Spectral Radius Books now! Available in PDF, ePub and Kindle.

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The Mutually Beneficial Relationship of Graphs and Matrices

Graphs and matrices enjoy a fascinating and mutually beneficial relationship. This interplay has benefited both graph theory and linear algebra. In one direction, knowledge about one of the graphs that can be associated with a matrix can be used to illuminate matrix properties and to get better information about the

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Inequalities for Graph Eigenvalues

Explores the inequalities for eigenvalues of the six matrices associated with graphs. Includes the main results and selected applications.

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Extremal Spectral Invariants of Graphs

We address several problems in spectral graph theory, with a common theme of optimizing or computing a spectral graph invariant, such as the spectral radius or spectral gap, over some family of graphs. In particular, we study measures of graph irregularity, we bound the adjacency spectral radius over all outerplanar

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The Joint Spectral Radius

This monograph is based on the Ph.D. Thesis of the author [58]. Its goal is twofold: First, it presents most researchwork that has been done during his Ph.D., or at least the part of the work that is related with the joint spectral radius. This work was concerned with

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Surveys in Combinatorics

Combinatorics is an active field of mathematical study and the British Combinatorial Conference, held biennially, aims to survey the most important developments by inviting distinguished mathematicians to lecture at the meeting. The contributions of the principal lecturers at the Seventh Conference, held in Cambridge, are published here and the topics

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