Algebraic Graph Theory

Algebraic Graph Theory Author : Norman Biggs
Release : 1993
Publisher : Cambridge University Press
ISBN : 9780521458979
File Size : 77.93 MB
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A revision of an important textbook: essential reading for all combinatorialists.

Topics in Algebraic Graph Theory

Topics in Algebraic Graph Theory Author : Lowell W. Beineke
Release : 2004-10-04
Publisher : Cambridge University Press
ISBN : 9780521801973
File Size : 76.69 MB
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There is no other book with such a wide scope of both areas of algebraic graph theory.

Algebraic Graph Theory

Algebraic Graph Theory Author : Chris Godsil
Release : 2013-12-01
Publisher : Springer Science & Business Media
ISBN : 1461301637
File Size : 27.60 MB
Format : PDF, Docs
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This book presents and illustrates the main tools and ideas of algebraic graph theory, with a primary emphasis on current rather than classical topics. It is designed to offer self-contained treatment of the topic, with strong emphasis on concrete examples.

Algebraic Graph Theory

Algebraic Graph Theory Author : Ulrich Knauer
Release : 2011-09-29
Publisher : Walter de Gruyter
ISBN : 311025509X
File Size : 71.6 MB
Format : PDF, ePub, Docs
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This is a highly self-contained book about algebraic graph theory which is written with a view to keep the lively and unconventional atmosphere of a spoken text to communicate the enthusiasm the author feels about this subject. The focus is on homomorphisms and endomorphisms, matrices and eigenvalues. Graph models are extremely useful for almost all applications and applicators as they play an important role as structuring tools. They allow to model net structures - like roads, computers, telephones - instances of abstract data structures - like lists, stacks, trees - and functional or object oriented programming.

Algebraic Graph Theory

Algebraic Graph Theory Author : Ulrich Knauer
Release : 2019-10-08
Publisher : Walter de Gruyter GmbH & Co KG
ISBN : 3110617366
File Size : 88.7 MB
Format : PDF, Kindle
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Graph models are extremely useful for a large number of applications as they play an important role as structuring tools. They allow to model net structures – like roads, computers, telephones, social networks – instances of abstract data structures – like lists, stacks, trees – and functional or object oriented programming. The focus of this highly self-contained book is on homomorphisms and endomorphisms, matrices and eigenvalues.

Algebra, Graph Theory and their Applications

Algebra, Graph Theory and their Applications Author : T.T Chelvam
Release : 2009-12-03
Publisher : ALPHA SCIENCE INTERNATIONAL LIMITED
ISBN : 8184873107
File Size : 20.67 MB
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Algebra and Graph Theory are two fascinating branches of Mathematics. The tools of each have been used in the other to explore and investigate problems in depth. Especially the Cayley graphs constructed out of the group structures have been greatly and extensively used in Parallel computers to provide network to the routing problem. ALGEBRA, GRAPH THEORY AND THEIR APPLICATIONS takes an inclusive view of the two areas and presents a wide range of topics. It includes sixteen referred research articles on algebra and graph theory of which three are expository in nature alongwith articles exhibiting the use of algebraic techniques in the study of graphs. A substantial proportion of the book covers topics that have not yet appeared in book form providing a useful resource to the younger generation of researchers in Discrete Mathematics.

Isomorphisms, Symmetry and Computations in Algebraic Graph Theory

Isomorphisms, Symmetry and Computations in Algebraic Graph Theory Author : Gareth A. Jones
Release : 2020-01-10
Publisher : Springer Nature
ISBN : 3030328082
File Size : 65.65 MB
Format : PDF, ePub, Mobi
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This book consists of a selection of peer-reviewed contributions to the Workshop on Algebraic Graph Theory that took place in Pilsen, Czech Republic in October 2016. Primarily intended for early career researchers, it presents eight self-contained articles on a selection of topics within algebraic combinatorics, ranging from association schemes to symmetries of graphs and isomorphism testing. Algebraic combinatorics is a compelling mathematical discipline based on the powerful interplay of algebraic and combinatorial methods. Algebraic interpretation of combinatorial structures (such as symmetry or regularity) has often led to enlightening discoveries and powerful results, while discrete and combinatorial structures have given rise to new algebraic structures that have found valuable applications. In addition to these original research contributions, the reader will find a survey linking numerous threads in algebraic combinatorics, and an extensive tutorial showcasing the universality of algebraic methods in the study of combinatorial structures.

Algebraic Graph Theory

Algebraic Graph Theory Author : Chris Godsil
Release : 2001-04-20
Publisher : Springer
ISBN : 9780387952413
File Size : 90.27 MB
Format : PDF, Mobi
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This book presents and illustrates the main tools and ideas of algebraic graph theory, with a primary emphasis on current rather than classical topics. It is designed to offer self-contained treatment of the topic, with strong emphasis on concrete examples.

Algebraic Graph Theory

Algebraic Graph Theory Author : Source Wikipedia
Release : 2013-09
Publisher : University-Press.org
ISBN : 9781230542928
File Size : 36.46 MB
Format : PDF
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Read : 778

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 32. Chapters: Adjacency algebra, Adjacency matrix, Algebraic connectivity, Alpha centrality, Cayley graph, Clustering coefficient, Conductance (graph), Conference graph, Conference matrix, Cycle space, Degree matrix, Distance-regular graph, Distance-transitive graph, Dual graph, Edge-transitive graph, Edge space, Frucht's theorem, Graph automorphism, Graph energy, Half-transitive graph, Ihara zeta function, Incidence matrix, Integral graph, Kirchhoff's theorem, Laplacian matrix, Lovasz conjecture, Mac Lane's planarity criterion, Matching polynomial, Modularity (networks), Parry-Sullivan invariant, Ramanujan graph, Rank (graph theory), Seidel adjacency matrix, Semi-symmetric graph, Spectral graph theory, Strongly regular graph, Tutte matrix, Two-graph, Vertex-transitive graph.

Isomorphisms, Symmetry and Computations in Algebraic Graph Theory

Isomorphisms, Symmetry and Computations in Algebraic Graph Theory Author : Gareth A. Jones
Release : 2021-02-21
Publisher : Springer
ISBN : 9783030328108
File Size : 56.79 MB
Format : PDF, Docs
Download : 210
Read : 1075

This book consists of a selection of peer-reviewed contributions to the Workshop on Algebraic Graph Theory that took place in Pilsen, Czech Republic in October 2016. Primarily intended for early career researchers, it presents eight self-contained articles on a selection of topics within algebraic combinatorics, ranging from association schemes to symmetries of graphs and isomorphism testing. Algebraic combinatorics is a compelling mathematical discipline based on the powerful interplay of algebraic and combinatorial methods. Algebraic interpretation of combinatorial structures (such as symmetry or regularity) has often led to enlightening discoveries and powerful results, while discrete and combinatorial structures have given rise to new algebraic structures that have found valuable applications. In addition to these original research contributions, the reader will find a survey linking numerous threads in algebraic combinatorics, and an extensive tutorial showcasing the universality of algebraic methods in the study of combinatorial structures.

Fundamentals of Algebraic Graph Transformation

Fundamentals of Algebraic Graph Transformation Author : Hartmut Ehrig
Release : 2006-05-01
Publisher : Springer Science & Business Media
ISBN : 3540311882
File Size : 72.52 MB
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This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. It contains an introduction to classical graphs. Basic and advanced results are first shown for an abstract form of replacement systems and are then instantiated to several forms of graph and Petri net transformation systems. The book develops typed attributed graph transformation and contains a practical case study.

Algebraic Graph Theory

Algebraic Graph Theory Author :
Release : 1992
Publisher :
ISBN :
File Size : 85.97 MB
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Some Results from Algebraic Graph Theory

Some Results from Algebraic Graph Theory Author : Jernej Azarija
Release : 2016
Publisher :
ISBN :
File Size : 21.53 MB
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In this thesis we present some results living in the intersection between graph theory and linear algebra. We introduce the subject of algebraic graph theory presenting some general results from this area. In particular we show how certain algebraic objects such as matrices and polynomials can be used to gain structural information about graphs. We then introduce two graph polynomials namely the chromatic polynomial and its generalization - the Tutte polynomial. We present a counterexample to a conjecture of J. Xu and Z. Liu about the chromatic polynomial and degree sequences. We then turn our attention to matrices associated with graphs namely the adjacency matrix and distance matrix. We present some results in the context of strongly regular graphs. In particular we show a connection between graphs maximizing the number of cycles with length matching their odd girth and Moore graphs. Continuing with strongly regular graphs we present a classificational result for strongly regular graphs. The approach is based on the so called star complement technique developed by Cvetković and Rowlinson.

Algebraic Graph Theory

Algebraic Graph Theory Author : Godlis
Release : 2005-01-01
Publisher :
ISBN : 9788181282620
File Size : 67.58 MB
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Algebraic Graph Theory

Algebraic Graph Theory Author : P Hell
Release : 1992
Publisher :
ISBN :
File Size : 58.12 MB
Format : PDF
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Topics in Spectral Analysis

Topics in Spectral Analysis Author : Donald Pierantozzi
Release : 2020-04-16
Publisher :
ISBN :
File Size : 51.8 MB
Format : PDF, Kindle
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Algebraic graph theory is the branch of mathematics that studies graphs by using algebraic properties of associated matrices. Spectral graph theory studies the relation between graph properties and the spectrum of the adjacency or Laplacian matrix.Google founders computed the Perron-Frobenius eigenvector of the web graph and became billionaires. The second largest eigenvalue of a graph gives information about expansion and randomness properties with smallest eigenvalue gives information about independence and chromatic number. Interlacing gives information about substructures. Eigenvalue multiplicities provides strong restrictions with the spectrum providing useful invariants.The standard material on spectra is first provided. Important applications of graph spectra involve the largest or second largest or smallest eigenvalue, or interlacing, topics are then presented. Special topics of trees, topological structures and spectral characterizations are discussed.Work herein is based on the PhD dissertation work at the University of Pennsylvania under the direction of former professors Bedrosian and Wilf with post-doctoral studies at Princeton University with professors Sarniak and Conway.DCP 11/19/19