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- Spectral Radius of Graphs

- 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have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author.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 : 212
- ISBN : 0128020970

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**Summary :** Written for mathematicians working with the theory of graph spectra, this book explores more than 400 inequalities for eigenvalues of the six matrices associated with finite simple graphs: the adjacency matrix, Laplacian matrix, signless Laplacian matrix, normalized Laplacian matrix, Seidel matrix, and distance matrix. The book begins with a brief survey ...

- Author : E.R. van Dam,R.E. Kooij
- Publisher : Unknown
- Release Date : 2006
- Total pages : 212
- ISBN : 0128020970

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**Summary :** 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 which was released on 2006. Get The Minimal Spectral Radius of Graphs with a Given Diameter Books now! Available in PDF, ePub and Kindle....

- Author : Thierry Lecroq,Laurent Mouchard
- Publisher : Springer
- Release Date : 2013-11-26
- Total pages : 474
- ISBN : 0128020970

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**Summary :** This book constitutes the thoroughly refereed post-workshop proceedings of the 24th International Workshop on Combinatorial Algorithms, IWOCA 2013, held in Rouen, France, in July 2013. The 33 revised full papers presented together with 10 short papers and 5 invited talks were carefully reviewed and selected from a total of 91 submissions. The papers are organized in ...

- Author : Peng Huang
- Publisher : Unknown
- Release Date : 2016
- Total pages : 71
- ISBN : 0128020970

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**Summary :** 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 ...

- Author : Frank Werner
- Publisher : MDPI
- Release Date : 2020-05-27
- Total pages : 294
- ISBN : 0128020970

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**Summary :** Graph theory is an important area of applied mathematics with a broad spectrum of applications in many fields. This book results from aSpecialIssue in the journal Mathematics entitled “Graph-Theoretic Problems and Their New Applications”. It contains 20 articles covering a broad spectrum of graph-theoretic works that were selected from 151 submitted papers ...

- Author : Angel Garrido
- Publisher : MDPI
- Release Date : 2020-03-05
- Total pages : 458
- ISBN : 0128020970

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**Summary :** Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry ...

- Author : Robin Chapman
- Publisher : Cambridge University Press
- Release Date : 2011-06-23
- Total pages : 437
- ISBN : 0128020970

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**Summary :** This volume contains nine survey articles based on the invited lectures given at the 23rd British Combinatorial Conference, held at Exeter in July 2011. This biennial conference is a well-established international event, with speakers from all over the world. By its nature, this volume provides an up-to-date overview of current research ...

- Author : Zoran Stanić
- Publisher : Walter de Gruyter GmbH & Co KG
- Release Date : 2017-04-24
- Total pages : 247
- ISBN : 0128020970

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**Summary :** Written for mathematicians working with the theory of graph spectra, this (primarily theoretical) book presents relevant results considering the spectral properties of regular graphs. The book begins with a short introduction including necessary terminology and notation. The author then proceeds with basic properties, specific subclasses of regular graphs (like distance-regular ...

- Author : Tai-He Fan,Shui-Li Chen,San-Min Wang,Yong-Ming Li
- Publisher : Springer
- Release Date : 2016-09-21
- Total pages : 679
- ISBN : 0128020970

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**Summary :** This book is the proceedings of the Fourth International Conference on Quantitative Logic and Soft Computing (QLSC2016) held 14-17, October, 2016 in Zhejiang Sci-Tech University, Hangzhou, China. It includes 61 papers, of which 5 are plenary talks( 3 abstracts and 2 full length talks). QLSC2016 was the fourth in a series of conferences on Quantitative ...

- Author : Dragan Stevanović,Pierre Hansen,Groupe d'études et de recherche en analyse des décisions (Montréal, Québec)
- Publisher : Unknown
- Release Date : 2007
- Total pages : 8
- ISBN : 0128020970

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**Summary :** 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 which was released on 2007. Get The Minimum Spectral Radius of Graphs with ...

- Author : S.K. Neogy,Ravindra B. Bapat,Dipti Dubey
- Publisher : Springer
- Release Date : 2018-11-28
- Total pages : 226
- ISBN : 0128020970

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**Summary :** This book discusses recent developments in mathematical programming and game theory, and the application of several mathematical models to problems in finance, games, economics and graph theory. All contributing authors are eminent researchers in their respective fields, from across the world. This book contains a collection of selected papers presented ...

- Author : Susanta Kumar Paikray,Hemen Dutta,John N. Mordeson
- Publisher : Springer Nature
- Release Date : 2021-06-28
- Total pages : 316
- ISBN : 0128020970

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**Summary :** The volume contains original research papers as the Proceedings of the International Conference on Advances in Mathematics and Computing, held at Veer Surendra Sai University of Technology, Odisha, India, on 7-8 February, 2020. It focuses on new trends in applied analysis, computational mathematics and related areas. It also includes certain new ...

- Author : D.M. Cvetkovic,M. Doob,I. Gutman,A. Torgašev
- Publisher : Elsevier
- Release Date : 1988-01-01
- Total pages : 305
- ISBN : 0128020970

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**Summary :** The purpose of this volume is to review the results in spectral graph theory which have appeared since 1978. The problem of characterizing graphs with least eigenvalue -2 was one of the original problems of spectral graph theory. The techniques used in the investigation of this problem have continued to be ...

- Author : Richard A. Brualdi,Ángeles Carmona,P. van den Driessche,Stephen Kirkland,Dragan Stevanović
- Publisher : Birkhäuser
- Release Date : 2018-03-31
- Total pages : 219
- ISBN : 0128020970

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**Summary :** This book contains the notes of the lectures delivered at an Advanced Course on Combinatorial Matrix Theory held at Centre de Recerca Matemàtica (CRM) in Barcelona. These notes correspond to five series of lectures. The first series is dedicated to the study of several matrix classes defined combinatorially, and ...