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Spectral Radius Of Graphs

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Spectral Radius of Graphs

Spectral Radius of Graphs Book
Author : Dragan Stevanovic
Publisher : Academic Press
Release : 2014-10-13
ISBN : 0128020970
Language : En, Es, Fr & De

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Book Description :

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have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author.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

The Minimal Spectral Radius of Graphs with a Given Diameter

The Minimal Spectral Radius of Graphs with a Given Diameter Book
Author : E.R. van Dam,R.E. Kooij
Publisher : Unknown
Release : 2006
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download The Minimal Spectral Radius of Graphs with a Given Diameter book written by E.R. van Dam,R.E. Kooij, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Inequalities for Graph Eigenvalues

Inequalities for Graph Eigenvalues Book
Author : Zoran Stanić
Publisher : Cambridge University Press
Release : 2015-07-23
ISBN : 1107545978
Language : En, Es, Fr & De

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Book Description :

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

Spectral Radius and Signless Laplacian Spectral Radius of K connected Graphs

Spectral Radius and Signless Laplacian Spectral Radius of K connected Graphs Book
Author : Peng Huang
Publisher : Unknown
Release : 2016
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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 many research field, such as computer science, communication network, information science and so on. In this thesis, we study k-connected graphs and focus on their spectral radius and signless Laplacian spectral radius. Firstly, we determine the graphs with maximum spectral radius among all k-connected graphs of fixed order with given diameter. As we know, when a graph is regular, its spectral radius and signless Laplacian spectral radius can easily be found. We obtain an upper bound on the signless Laplacian spectral radius of k-connected irregular graphs. Finally, we give some other results mainly related to the signless Laplacian matrix.

Graph Theoretic Problems and Their New Applications

Graph Theoretic Problems and Their New Applications Book
Author : Frank Werner
Publisher : MDPI
Release : 2020-05-27
ISBN : 3039287982
Language : En, Es, Fr & De

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Book Description :

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 of graphs, domination games, contraction mappings, and neutrosophic graphs. Several applications of graph theory are discussed, e.g., the use of graph theory in the context of molecular processes.

Combinatorial Algorithms

Combinatorial Algorithms Book
Author : Thierry Lecroq,Laurent Mouchard
Publisher : Springer
Release : 2013-11-26
ISBN : 3642452787
Language : En, Es, Fr & De

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Book Description :

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 Book
Author : Teresa W. Haynes,Stephen T. Hedetniemi,Michael A. Henning
Publisher : Springer Nature
Release : 2021-05-04
ISBN : 3030588920
Language : En, Es, Fr & De

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Book Description :

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 signed, minus and majority domination, power domination, and alliances in graphs. The third part also includes a chapter on self-stabilizing algorithms. Of extra benefit to the reader, the first chapter includes a glossary of commonly used terms. The book is intended to provide a reference for established researchers in the fields of domination and graph theory and graduate students who wish to gain knowledge of the topics covered as well as an overview of the major accomplishments and proof techniques used in the field.

The Minimum Spectral Radius of Graphs with a Given Clique Number

The Minimum Spectral Radius of Graphs with a Given Clique Number Book
Author : Dragan Stevanović,Pierre Hansen,Groupe d'études et de recherche en analyse des décisions (Montréal, Québec)
Publisher : Unknown
Release : 2007
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download The Minimum Spectral Radius of Graphs with a Given Clique Number book written by Dragan Stevanović,Pierre Hansen,Groupe d'études et de recherche en analyse des décisions (Montréal, Québec), available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Discrete Mathematics and Symmetry

Discrete Mathematics and Symmetry Book
Author : Angel Garrido
Publisher : MDPI
Release : 2020-03-05
ISBN : 3039281909
Language : En, Es, Fr & De

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Book Description :

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 means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group.

Surveys in Combinatorics 2011

Surveys in Combinatorics 2011 Book
Author : Robin Chapman
Publisher : Cambridge University Press
Release : 2011-06-23
ISBN : 1139503685
Language : En, Es, Fr & De

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Book Description :

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 activity in several areas of combinatorics, including extremal graph theory, the cyclic sieving phenomenon and transversals in Latin squares. Each article is clearly written and assumes little prior knowledge on the part of the reader. The authors are some of the world's foremost researchers in their fields, and here they summarise existing results and give a unique preview of the most recent developments. The book provides a valuable survey of the present state of knowledge in combinatorics. It will be useful to research workers and advanced graduate students, primarily in mathematics but also in computer science and statistics.

Quantitative Logic and Soft Computing 2016

Quantitative Logic and Soft Computing 2016 Book
Author : Tai-He Fan,Shui-Li Chen,San-Min Wang,Yong-Ming Li
Publisher : Springer
Release : 2016-09-21
ISBN : 3319462067
Language : En, Es, Fr & De

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Book Description :

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 Logic and Soft Computing. This conference was a major symposium for scientists, engineers and practitioners to present their updated results, ideas, developments and applications in all areas of quantitative logic and soft computing. The book aims to strengthen relations between industry research laboratories and universities in fields such as quantitative logic and soft computing worldwide as follows: (1) Quantitative Logic and Uncertainty Logic; (2) Automata and Quantification of Software; (3) Fuzzy Connectives and Fuzzy Reasoning; (4) Fuzzy Logical Algebras; (5) Artificial Intelligence and Soft Computing; (6) Fuzzy Sets Theory and Applications.

Algorithms and Discrete Applied Mathematics

Algorithms and Discrete Applied Mathematics Book
Author : Sathish Govindarajan,Anil Maheshwari
Publisher : Springer
Release : 2016-02-12
ISBN : 3319292218
Language : En, Es, Fr & De

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Book Description :

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 discrete mathematics.

On the Spectral Radius of Graphs with a Given Domination Number

On the Spectral Radius of Graphs with a Given Domination Number Book
Author : Dragan Stevanović,Pierre Hansen,Mustapha Aouchiche,Groupe d'études et de recherche en analyse des décisions (Montréal, Québec)
Publisher : Unknown
Release : 2007
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download On the Spectral Radius of Graphs with a Given Domination Number book written by Dragan Stevanović,Pierre Hansen,Mustapha Aouchiche,Groupe d'études et de recherche en analyse des décisions (Montréal, Québec), available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Recent Results in the Theory of Graph Spectra

Recent Results in the Theory of Graph Spectra Book
Author : D.M. Cvetkovic,M. Doob,I. Gutman,A. Torgašev
Publisher : Elsevier
Release : 1988-01-01
ISBN : 9780080867762
Language : En, Es, Fr & De

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Book Description :

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 useful in other contexts including forbidden subgraph techniques as well as geometric methods involving root systems. In the meantime, the particular problem giving rise to these methods has been solved almost completely. This is indicated in Chapter 1. The study of various combinatorial objects (including distance regular and distance transitive graphs, association schemes, and block designs) have made use of eigenvalue techniques, usually as a method to show the nonexistence of objects with certain parameters. The basic method is to construct a graph which contains the structure of the combinatorial object and then to use the properties of the eigenvalues of the graph. Methods of this type are given in Chapter 2. Several topics have been included in Chapter 3, including the relationships between the spectrum and automorphism group of a graph, the graph isomorphism and the graph reconstruction problem, spectra of random graphs, and the Shannon capacity problem. Some graph polynomials related to the characteristic polynomial are described in Chapter 4. These include the matching, distance, and permanental polynomials. Applications of the theory of graph spectra to Chemistry and other branches of science are described from a mathematical viewpoint in Chapter 5. The last chapter is devoted to the extension of the theory of graph spectra to infinite graphs.

Graphs with Given Diameter Maximizing the Spectral Radius

Graphs with Given Diameter Maximizing the Spectral Radius Book
Author : E.R. van Dam
Publisher : Unknown
Release : 2007
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Graphs with Given Diameter Maximizing the Spectral Radius book written by E.R. van Dam, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Combinatorial Matrix Theory

Combinatorial Matrix Theory Book
Author : Richard A. Brualdi,Ángeles Carmona,P. van den Driessche,Stephen Kirkland,Dragan Stevanović
Publisher : Birkhäuser
Release : 2018-03-31
ISBN : 3319709534
Language : En, Es, Fr & De

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Book Description :

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 was delivered by Richard A. Brualdi. The second one, given by Pauline van den Driessche, is concerned with the study of spectral properties of matrices with a given sign pattern. Dragan Stevanović delivered the third one, devoted to describing the spectral radius of a graph as a tool to provide bounds of parameters related with properties of a graph. The fourth lecture was delivered by Stephen Kirkland and is dedicated to the applications of the Group Inverse of the Laplacian matrix. The last one, given by Ángeles Carmona, focuses on boundary value problems on finite networks with special in-depth on the M-matrix inverse problem.

Asymptotic Results on the Spectral Radius and the Diameter of Graphs

Asymptotic Results on the Spectral Radius and the Diameter of Graphs Book
Author : Sebastian M. Cioabǎ
Publisher : Unknown
Release : 2008
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Asymptotic Results on the Spectral Radius and the Diameter of Graphs book written by Sebastian M. Cioabǎ, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Matrices in Combinatorics and Graph Theory

Matrices in Combinatorics and Graph Theory Book
Author : Bolian Liu,Hong-Jian Lai
Publisher : Springer Science & Business Media
Release : 2013-03-09
ISBN : 1475731655
Language : En, Es, Fr & De

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Book Description :

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 proving theorems which, at least on the surface, are combinatorial in nature. In the book by Liu and Lai, this picture is enlarged and expanded to include recent developments and contributions of Chinese mathematicians, many of which have not been readily available to those of us who are unfamiliar with Chinese journals. Necessarily, there is some overlap with the book Combinatorial Matrix Theory. Some of the additional topics include: spectra of graphs, eulerian graph problems, Shannon capacity, generalized inverses of Boolean matrices, matrix rearrangements, and matrix completions. A topic to which many Chinese mathematicians have made substantial contributions is the combinatorial analysis of powers of nonnegative matrices, and a large chapter is devoted to this topic. This book should be a valuable resource for mathematicians working in the area of combinatorial matrix theory. Richard A. Brualdi University of Wisconsin - Madison 1 Linear Alg. Applies., vols. 162-4, 1992, 65-105 2Camhridge University Press, 1991.

Graphs and Matrices

Graphs and Matrices Book
Author : Ravindra B. Bapat
Publisher : Springer Science & Business Media
Release : 2010-07-23
ISBN : 1848829817
Language : En, Es, Fr & De

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Book Description :

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 include those of graph theory such as regular graphs and algebraic connectivity, Laplacian eigenvalues of threshold graphs, positive definite completion problem and graph-based matrix games. Whilst this book will be invaluable to researchers in graph theory, it may also be of benefit to a wider, cross-disciplinary readership.

Topics in Algebraic Graph Theory

Topics in Algebraic Graph Theory Book
Author : Lowell W. Beineke,Robin J. Wilson,Senior Lecturer Faculty of Mathematics Robin J Wilson,Peter J. Cameron
Publisher : Cambridge University Press
Release : 2004-10-04
ISBN : 9780521801973
Language : En, Es, Fr & De

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Book Description :

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