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have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author.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

Produk Detail:

  • Author : Dragan Stevanovic
  • Publisher : Academic Press
  • Pages : 166 pages
  • ISBN : 0128020970
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKSpectral Radius of Graphs

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,

Spectra of Graphs

Spectra of Graphs
  • Author : Dragos M. Cvetkovic,Dragoš M. Cvetković,Michael Doob,Horst Sachs
  • Publisher : Unknown Publisher
  • Release : 02 July 1980
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

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

Graphs and Matrices

Graphs and Matrices
  • Author : Ravindra B. Bapat
  • Publisher : Springer
  • Release : 19 September 2014
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,

Spectral Radius and Signless Laplacian Spectral Radius of K-connected Graphs

Spectral Radius and Signless Laplacian Spectral Radius of K-connected Graphs
  • Author : Peng Huang
  • Publisher : Unknown Publisher
  • Release : 02 July 2022
GET THIS BOOKSpectral 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 the eigenvalues of the adjacency matrix and the signless Laplacian matrix, respectively. These two matrices of a graph have been studied for several decades since they have been applied to

Graph-Theoretic Problems and Their New Applications

Graph-Theoretic Problems and Their New Applications
  • Author : Frank Werner
  • Publisher : MDPI
  • Release : 27 May 2020
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

Structures of Domination in Graphs

Structures of Domination in Graphs
  • Author : Teresa W. Haynes,Stephen T. Hedetniemi,Michael A. Henning
  • Publisher : Springer Nature
  • Release : 04 May 2021
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

Matrices in Combinatorics and Graph Theory

Matrices in Combinatorics and Graph Theory
  • Author : Bolian Liu,Hong-Jian Lai
  • Publisher : Springer Science & Business Media
  • Release : 09 March 2013
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

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

Spectral Algorithms

Spectral Algorithms
  • Author : Ravindran Kannan,Santosh Vempala
  • Publisher : Now Publishers Inc
  • Release : 02 July 2022
GET THIS BOOKSpectral Algorithms

Spectral methods refer to the use of eigenvalues, eigenvectors, singular values and singular vectors. They are widely used in Engineering, Applied Mathematics and Statistics. More recently, spectral methods have found numerous applications in Computer Science to "discrete" as well "continuous" problems. Spectral Algorithms describes modern applications of spectral methods, and novel algorithms for estimating spectral parameters. The first part of the book presents applications of spectral methods to problems from a variety of topics including combinatorial optimization, learning and clustering.

Algorithms and Discrete Applied Mathematics

Algorithms and Discrete Applied Mathematics
  • Author : Sathish Govindarajan,Anil Maheshwari
  • Publisher : Springer
  • Release : 12 February 2016
GET THIS BOOKAlgorithms and Discrete Applied Mathematics

This book collects the refereed proceedings of the Second International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2016, held in Thiruvananthapuram, India, in February 2016. The volume contains 30 full revised papers from 90 submissions along with 1 invited talk presented at the conference. The conference focuses on topics related to efficient algorithms and data structures, their analysis (both theoretical and experimental) and the mathematical problems arising thereof, and new applications of discrete mathematics, advances in existing applications and development of new tools for

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 : 25 January 2012
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 of Graphs is a compilation of many of the exciting results concerning Laplacian matrices developed since the mid 1970s by well-known mathematicians such as Fallat, Fiedler, Grone, Kirkland, Merris, Mohar,