Graphs With Few Eigenvalues An Interplay Between Combinatorics And Algebra
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Graphs With Few Eigenvalues An Interplay Between Combinatorics And Algebra
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Author : Edwin R. van Dam
language : en
Publisher:
Release Date : 1996
Graphs With Few Eigenvalues An Interplay Between Combinatorics And Algebra written by Edwin R. van Dam and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
Eigenvalues Multiplicities And Graphs
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Author : Charles R. Johnson
language : en
Publisher: Cambridge University Press
Release Date : 2018-02-12
Eigenvalues Multiplicities And Graphs written by Charles R. Johnson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-12 with Mathematics categories.
This book investigates the influence of the graph of a symmetric matrix on the multiplicities of its eigenvalues.
The Mutually Beneficial Relationship Of Graphs And Matrices
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Author : Richard A. Brualdi
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-07-06
The Mutually Beneficial Relationship Of Graphs And Matrices written by Richard A. Brualdi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-06 with Mathematics categories.
Graphs and matrices enjoy a fascinating and mutually beneficial relationship. This interplay has benefited both graph theory and linear algebra. In one direction, knowledge about one of the graphs that can be associated with a matrix can be used to illuminate matrix properties and to get better information about the matrix. Examples include the use of digraphs to obtain strong results on diagonal dominance and eigenvalue inclusion regions and the use of the Rado-Hall theorem to deduce properties of special classes of matrices. Going the other way, linear algebraic properties of one of the matrices associated with a graph can be used to obtain useful combinatorial information about the graph. The adjacency matrix and the Laplacian matrix are two well-known matrices associated to a graph, and their eigenvalues encode important information about the graph. Another important linear algebraic invariant associated with a graph is the Colin de Verdiere number, which, for instance, characterizes certain topological properties of the graph. This book is not a comprehensive study of graphs and matrices. The particular content of the lectures was chosen for its accessibility, beauty, and current relevance, and for the possibility of enticing the audience to want to learn more.
Eigenspaces Of Graphs
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Author : Dragoš M. Cvetković
language : en
Publisher: Cambridge University Press
Release Date : 1997-01-09
Eigenspaces Of Graphs written by Dragoš M. Cvetković and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-09 with Mathematics categories.
Current research on the spectral theory of finite graphs may be seen as part of a wider effort to forge closer links between algebra and combinatorics (in particular between linear algebra and graph theory).This book describes how this topic can be strengthened by exploiting properties of the eigenspaces of adjacency matrices associated with a graph. The extension of spectral techniques proceeds at three levels: using eigenvectors associated with an arbitrary labelling of graph vertices, using geometrical invariants of eigenspaces such as graph angles and main angles, and introducing certain kinds of canonical eigenvectors by means of star partitions and star bases. One objective is to describe graphs by algebraic means as far as possible, and the book discusses the Ulam reconstruction conjecture and the graph isomorphism problem in this context. Further problems of graph reconstruction and identification are used to illustrate the importance of graph angles and star partitions in relation to graph structure. Specialists in graph theory will welcome this treatment of important new research.
Inequalities For Graph Eigenvalues
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Author : Zoran Stanić
language : en
Publisher: Cambridge University Press
Release Date : 2015-07-23
Inequalities For Graph Eigenvalues written by Zoran Stanić and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-23 with Mathematics categories.
This book explores the inequalities for eigenvalues of the six matrices associated with graphs. Includes the main results and selected applications.
Spectral Generalizations Of Line Graphs
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Author : Dragoš Cvetkovic
language : en
Publisher: Cambridge University Press
Release Date : 2004-07-22
Spectral Generalizations Of Line Graphs written by Dragoš Cvetkovic and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-22 with Mathematics categories.
Introduction -- Forbidden subgraphs -- Root systems -- Regular graphs -- Star complements -- The Maximal exceptional graphs -- Miscellaneous results.
Advanced Graph Theory And Combinatorics
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Author : Michel Rigo
language : en
Publisher: John Wiley & Sons
Release Date : 2016-11-22
Advanced Graph Theory And Combinatorics written by Michel Rigo and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-22 with Computers categories.
Advanced Graph Theory focuses on some of the main notions arising in graph theory with an emphasis from the very start of the book on the possible applications of the theory and the fruitful links existing with linear algebra. The second part of the book covers basic material related to linear recurrence relations with application to counting and the asymptotic estimate of the rate of growth of a sequence satisfying a recurrence relation.
Distance Regular Graphs
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Author : Andries E. Brouwer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Distance Regular Graphs written by Andries E. Brouwer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Ever since the discovery of the five platonic solids in ancient times, the study of symmetry and regularity has been one of the most fascinating aspects of mathematics. Quite often the arithmetical regularity properties of an object imply its uniqueness and the existence of many symmetries. This interplay between regularity and symmetry properties of graphs is the theme of this book. Starting from very elementary regularity properties, the concept of a distance-regular graph arises naturally as a common setting for regular graphs which are extremal in one sense or another. Several other important regular combinatorial structures are then shown to be equivalent to special families of distance-regular graphs. Other subjects of more general interest, such as regularity and extremal properties in graphs, association schemes, representations of graphs in euclidean space, groups and geometries of Lie type, groups acting on graphs, and codes are covered independently. Many new results and proofs and more than 750 references increase the encyclopaedic value of this book.
Journal Of Algebraic Combinatorics
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Author :
language : en
Publisher:
Release Date : 1999
Journal Of Algebraic Combinatorics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Algebra categories.
A First Course In Graph Theory And Combinatorics
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Author : Sebastian M. Cioabă
language : en
Publisher: Springer
Release Date : 2009-05-15
A First Course In Graph Theory And Combinatorics written by Sebastian M. Cioabă and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-15 with Mathematics categories.
The concept of a graph is fundamental in mathematics since it conveniently encodes diverse relations and facilitates combinatorial analysis of many complicated counting problems. In this book, the authors have traced the origins of graph theory from its humble beginnings of recreational mathematics to its modern setting for modeling communication networks as is evidenced by the World Wide Web graph used by many Internet search engines. This book is an introduction to graph theory and combinatorial analysis. It is based on courses given by the second author at Queen's University at Kingston, Ontario, Canada between 2002 and 2008. The courses were aimed at students in their final year of their undergraduate program.