Spectral Radius of Graphs

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  • Publisher : Academic Press
  • Release : 13 October 2014
  • ISBN : 9780128020975
  • Page : 166 pages
  • Rating : 4.5/5 from 103 voters

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have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author.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

Spectral Radius of Graphs
  • Author : Dragan Stevanovic
  • Publisher : Academic Press
  • Release Date : 2014-10-13
  • ISBN : 9780128020975
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 : Dragos M. Cvetkovic,Dragoš M. Cvetković,Michael Doob,Horst Sachs
  • Publisher : Unknown
  • Release Date : 1980
  • ISBN : UOM:39015040419585
GET THIS BOOKSpectra of Graphs

The theory of graph spectra can, in a way, be considered as an attempt to utilize linear algebra including, in particular, the well-developed theory of matrices for the purposes of graph theory and its applications. However, that does not mean that the theory of graph spectra can be reduced to the theory of matrices; on the contrary, it has its own characteristic features and specific ways of reasoning fully justifying it to be treated as a theory in its own

Inequalities for Graph Eigenvalues

Inequalities for Graph Eigenvalues
  • Author : Zoran Stanić
  • Publisher : Cambridge University Press
  • Release Date : 2015-07-23
  • ISBN : 9781107545977
GET THIS BOOKInequalities for Graph Eigenvalues

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

The Minimal Spectral Radius of Graphs with a Given Diameter

The Minimal Spectral Radius of Graphs with a Given Diameter
  • Author : E.R. van Dam,R.E. Kooij
  • Publisher : Unknown
  • Release Date : 2006
  • ISBN : OCLC:150296670
GET THIS BOOKThe Minimal Spectral Radius of Graphs with a Given Diameter

Spectra of Graphs

Spectra of Graphs
  • Author : Andries E. Brouwer,Willem H. Haemers
  • Publisher : Springer Science & Business Media
  • Release Date : 2011-12-17
  • ISBN : 9781461419396
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

The Joint Spectral Radius

The Joint Spectral Radius
  • Author : Raphaël Jungers
  • Publisher : Springer
  • Release Date : 2009-05-15
  • ISBN : 9783540959809
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

Eigenspaces of Graphs

Eigenspaces of Graphs
  • Author : Dragos Cvetkovic,Dragoš M. Cvetković,Peter Rowlinson,Slobodan Simic
  • Publisher : Cambridge University Press
  • Release Date : 1997-01-09
  • ISBN : 0521573521
GET THIS BOOKEigenspaces of Graphs

This book describes the spectral theory of finite graphs.

Spectral Analysis on Graph-like Spaces

Spectral Analysis on Graph-like Spaces
  • Author : Olaf Post
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-01-06
  • ISBN : 9783642238390
GET THIS BOOKSpectral Analysis on Graph-like Spaces

Small-radius tubular structures have attracted considerable attention in the last few years, and are frequently used in different areas such as Mathematical Physics, Spectral Geometry and Global Analysis. In this monograph, we analyse Laplace-like operators on thin tubular structures ("graph-like spaces''), and their natural limits on metric graphs. In particular, we explore norm resolvent convergence, convergence of the spectra and resonances. Since the underlying spaces in the thin radius limit change, and become singular in the limit, we develop new

Graphs and Matrices

Graphs and Matrices
  • Author : Ravindra B. Bapat
  • Publisher : Springer
  • Release Date : 2014-09-19
  • ISBN : 9781447165699
GET THIS BOOKGraphs and Matrices

This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs,

The Minimum Spectral Radius of Graphs with a Given Clique Number

The Minimum Spectral Radius of Graphs with a Given Clique Number
  • Author : Dragan Stevanović,Pierre Hansen,Groupe d'études et de recherche en analyse des décisions (Montréal, Québec)
  • Publisher : Unknown
  • Release Date : 2007
  • ISBN : OCLC:165866111
GET THIS BOOKThe Minimum Spectral Radius of Graphs with a Given Clique Number

Graph Spectra for Complex Networks

Graph Spectra for Complex Networks
  • Author : Piet van Mieghem
  • Publisher : Cambridge University Press
  • Release Date : 2010-12-02
  • ISBN : 9781139492270
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

Random Walks on Infinite Graphs and Groups

Random Walks on Infinite Graphs and Groups
  • Author : Wolfgang Woess
  • Publisher : Cambridge University Press
  • Release Date : 2000-02-13
  • ISBN : 9780521552929
GET THIS BOOKRandom Walks on Infinite Graphs and Groups

The main theme of this book is the interplay between random walks and discrete structure theory.

Graph-Theoretic Problems and Their New Applications

Graph-Theoretic Problems and Their New Applications
  • Author : Frank Werner
  • Publisher : MDPI
  • Release Date : 2020-05-27
  • ISBN : 9783039287987
GET THIS BOOKGraph-Theoretic Problems and Their New Applications

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 after a thorough refereeing process. Among others, it includes a deep survey on mixed graphs and their use for solutions ti scheduling problems. Other subjects include topological indices, domination numbers

Combinatorial Algorithms

Combinatorial Algorithms
  • Author : Thierry Lecroq,Laurent Mouchard
  • Publisher : Springer
  • Release Date : 2013-11-26
  • ISBN : 9783642452789
GET THIS BOOKCombinatorial Algorithms

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 topical sections on algorithms on graphs; algorithms on strings; discrete geometry and satisfiability.

Structures of Domination in Graphs

Structures of Domination in Graphs
  • Author : Teresa W. Haynes,Stephen T. Hedetniemi,Michael A. Henning
  • Publisher : Springer Nature
  • Release Date : 2021-05-04
  • ISBN : 9783030588922
GET THIS BOOKStructures of Domination in Graphs

This volume comprises 17 contributions that present advanced topics in graph domination, featuring open problems, modern techniques, and recent results. The book is divided into 3 parts. The first part focuses on several domination-related concepts: broadcast domination, alliances, domatic numbers, dominator colorings, irredundance in graphs, private neighbor concepts, game domination, varieties of Roman domination and spectral graph theory. The second part covers domination in hypergraphs, chessboards, and digraphs and tournaments. The third part focuses on the development of algorithms and complexity of