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Spectral Radius of Graphs

Spectral Radius of Graphs
  • Author : Dragan Stevanovic
  • Publsiher : Academic Press
  • Release : 13 October 2014
  • ISBN : 0128020970
  • Pages : 166 pages
  • Rating : 4/5 from 21 ratings
GET THIS BOOKSpectral Radius of Graphs

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have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author.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 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
  • Author : Dragan Stevanovic
  • Publisher : Academic Press
  • Release : 13 October 2014
GET THIS BOOKSpectral 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 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,


Spectral Radius of Graphs

Spectral Radius of Graphs
  • Author : Dragan Stevanovic
  • Publisher : Academic Press
  • Release : 08 October 2014
GET THIS BOOKSpectral 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 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,




Spectra of Graphs

Spectra of Graphs
  • Author : Andries E. Brouwer,Willem H. Haemers
  • Publisher : Springer Science & Business Media
  • Release : 17 December 2011
GET THIS BOOKSpectra 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 the end of each chapter provide practice and vary from easy yet interesting applications of the treated theory, to little excursions into related topics. Tables, references at the end of


Matrices in Combinatorics and Graph Theory

Matrices in Combinatorics and Graph Theory
  • Author : Bolian Liu,Hong-Jian Lai
  • Publisher : Springer Science & Business Media
  • Release : 31 October 2000
GET THIS BOOKMatrices in Combinatorics and Graph Theory

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 entitled Combinatorial Matrix Theon? where an attempt was made to give a broad picture of the use of combinatorial ideas in matrix theory and the use of matrix theory in



Surveys in Combinatorics

Surveys in Combinatorics
  • Author : B. Bollobás
  • Publisher : Cambridge University Press
  • Release : 09 August 1979
GET THIS BOOKSurveys 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 reflect the breadth of the subject. Each author has written a broadly conceived survey, not limited to his own work, but intended for wide readership. Important aspects of the subject



Graphs and Matrices

Graphs and Matrices
  • Author : Ravindra B. Bapat
  • Publisher : Springer Science & Business Media
  • Release : 23 July 2010
GET THIS BOOKGraphs and Matrices

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 the view of leading the student into further research. In the first part of the book matrix preliminaries are discussed and the basic properties of graph-associated matrices highlighted. Further topics


The Joint Spectral Radius

The Joint Spectral Radius
  • Author : Raphaël Jungers
  • Publisher : Springer
  • Release : 15 May 2009
GET THIS BOOKThe 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 theoretical developments (part I) as well as the study of some applications (part II). As a second goal, it was the author’s feeling that a survey on the state



Fractional Graph Theory

Fractional Graph Theory
  • Author : Edward R. Scheinerman,Daniel H. Ullman
  • Publisher : Courier Corporation
  • Release : 29 April 2013
GET THIS BOOKFractional Graph Theory

This volume explains the general theory of hypergraphs and presents in-depth coverage of fundamental and advanced topics: fractional matching, fractional coloring, fractional edge coloring, fractional arboricity via matroid methods, fractional isomorphism, and more. 1997 edition.


Graph Spectra for Complex Networks

Graph Spectra for Complex Networks
  • Author : Piet van Mieghem
  • Publisher : Cambridge University Press
  • Release : 02 December 2010
GET THIS BOOKGraph Spectra for Complex Networks

Analyzing the behavior of complex networks is an important element in the design of new man-made structures such as communication systems and biologically engineered molecules. Because any complex network can be represented by a graph, and therefore in turn by a matrix, graph theory has become a powerful tool in the investigation of network performance. This self-contained 2010 book provides a concise introduction to the theory of graph spectra and its applications to the study of complex networks. Covering a range


Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs

Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs
  • Author : Jason J. Molitierno
  • Publisher : CRC Press
  • Release : 19 April 2016
GET THIS BOOKApplications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs

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 o