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- Author : Dragan Stevanovic
- Publsiher : Academic Press
- Release : 13 October 2014
- ISBN : 0128020970
- Pages : 166 pages
- Rating : 4/5 from 21 reviews

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Read or download book entitled Spectral Radius of Graphs written by Dragan Stevanovic which was release on 13 October 2014, this book published by Academic Press. Available in PDF, EPUB and Kindle Format. Book excerpt: 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have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author.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

- Author : Dragan Stevanovic
- Publisher : Academic Press
- Release Date : 2014-10-13
- Total pages : 166
- ISBN : 0128020970

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**Summary :** 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 ...

- Author : Zoran Stanić
- Publisher : Cambridge University Press
- Release Date : 2015-07-23
- Total pages : 312
- ISBN : 0128020970

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

- Author : Bolian Liu,Hong-Jian Lai
- Publisher : Springer Science & Business Media
- Release Date : 2000-10-31
- Total pages : 310
- ISBN : 0128020970

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**Summary :** Combinatorics and Matrix Theory have a symbiotic, or mutually beneficial, relationship. This relationship is discussed in my paper The symbiotic relationship of combinatorics and matrix theoryl where I attempted to justify this description. One could say that a more detailed justification was given in my book with H. J. Ryser ...

- Author : Ravindra B. Bapat
- Publisher : Springer Science & Business Media
- Release Date : 2010-07-23
- Total pages : 171
- ISBN : 0128020970

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**Summary :** Graphs and Matrices provides a welcome addition to the rapidly expanding selection of literature in this field. As the title suggests, the book’s primary focus is graph theory, with an emphasis on topics relating to linear algebra and matrix theory. Information is presented at a relatively elementary level with ...

- Author : Anonim
- Publisher : Unknown
- Release Date : 2008
- Total pages : 212
- ISBN : 0128020970

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**Summary :** Download or read online Match written by , published by which was released on 2008. Get Match Books now! Available in PDF, ePub and Kindle....

- Author : Richard A. Brualdi
- Publisher : American Mathematical Soc.
- Release Date : 2011-07-06
- Total pages : 96
- ISBN : 0128020970

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**Summary :** 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 ...

- Author : Anonim
- Publisher : Unknown
- Release Date : 2008
- Total pages : 212
- ISBN : 0128020970

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**Summary :** Download or read online Ars Combinatoria written by , published by which was released on 2008. Get Ars Combinatoria Books now! Available in PDF, ePub and Kindle....

- Author : Lowell W. Beineke,Robin J. Wilson,Senior Lecturer Faculty of Mathematics Robin J Wilson,Peter J. Cameron
- Publisher : Cambridge University Press
- Release Date : 2004-10-04
- Total pages : 276
- ISBN : 0128020970

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**Summary :** There is no other book with such a wide scope of both areas of algebraic graph theory....

- Author : Anonim
- Publisher : Unknown
- Release Date : 2008
- Total pages : 212
- ISBN : 0128020970

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**Summary :** Download or read online Mathematical Reviews written by , published by which was released on 2008. Get Mathematical Reviews Books now! Available in PDF, ePub and Kindle....

- Author : Anonim
- Publisher : Unknown
- Release Date : 1996
- Total pages : 212
- ISBN : 0128020970

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**Summary :** Download or read online Mathematica Japonicae written by , published by which was released on 1996. Get Mathematica Japonicae Books now! Available in PDF, ePub and Kindle....

- Author : Raphaël Jungers
- Publisher : Springer
- Release Date : 2009-05-15
- Total pages : 146
- ISBN : 0128020970

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**Summary :** 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 ...

- Author : Erxiong Jiang,Chuan-Long Wang
- Publisher : Unknown
- Release Date : 2008
- Total pages : 488
- ISBN : 0128020970

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**Summary :** Download or read online Advances in Matrix Theory and Its Applications written by Erxiong Jiang,Chuan-Long Wang, published by which was released on 2008. Get Advances in Matrix Theory and Its Applications Books now! Available in PDF, ePub and Kindle....

- Author : Matematički institut (Belgrade, Serbia)
- Publisher : Unknown
- Release Date : 1989
- Total pages : 212
- ISBN : 0128020970

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**Summary :** Download or read online Publications de L Institut Math matique written by Matematički institut (Belgrade, Serbia), published by which was released on 1989. Get Publications de L Institut Math matique Books now! Available in PDF, ePub and Kindle....

- Author : Matematički institut (Belgrade, Serbia)
- Publisher : Unknown
- Release Date : 1986
- Total pages : 212
- ISBN : 0128020970

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**Summary :** Download or read online Publications de L Institut Mathe atique written by Matematički institut (Belgrade, Serbia), published by which was released on 1986. Get Publications de L Institut Mathe atique Books now! Available in PDF, ePub and Kindle....

- Author : Jason J. Molitierno
- Publisher : CRC Press
- Release Date : 2012-01-25
- Total pages : 425
- ISBN : 0128020970

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**Summary :** On the surface, matrix theory and graph theory seem like very different branches of mathematics. However, adjacency, Laplacian, and incidence matrices are commonly used to represent graphs, and many properties of matrices can give us useful information about the structure of graphs. Applications of Combinatorial Matrix Theory to Laplacian Matrices ...