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Topic: Algebraic graph theory


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In the News (Fri 19 Jul 19)

  
  Graph theory - Wikipedia, the free encyclopedia
Informally, a graph is a set of objects called vertices (or nodes) connected by links called edges (or arcs) which can be directed (assigned a direction).
Graphs are represented graphically by drawing a dot for every vertex, and drawing an arc between two vertices if they are connected by an edge.
A graph drawing should not be confused with the graph itself (the abstract, non-graphical structure) as there are several ways to structure the graph drawing.
en.wikipedia.org /wiki/Graph_theory   (1209 words)

  
 Algebraic graph theory - Wikipedia, the free encyclopedia
Algebraic graph theory is a branch of mathematics.
In one sense, algebraic graph theory studies graphs in connection with linear algebra.
This part of algebraic graph theory is also called the spectral graph theory.
en.wikipedia.org /wiki/Algebraic_graph_theory   (144 words)

  
 >☞ > Buy best Algebraic Graph Theory Algebraic Graph Theory cheapest in Books   (Site not responding. Last check: 2007-11-05)
This book is primarily aimed at graduate students and researchers in graph theory, combinatorics, or discrete mathematics in general.
However, all the necessary graph theory is developed from scratch, so the only pre-requisite for reading it is a first course in linear algebra and a small amount of elementary group theory.
--It is sketchy on chromatic polynomial, planar graph.
www.javadot.com /algebraic-graph-theory,0387952209_i.htm   (228 words)

  
 Algebraic Graph Theory Scientific Programme   (Site not responding. Last check: 2007-11-05)
Other results include the assertion that a connected graph with least eigenvalue -2 is exceptional if and only if it has an exceptional star complement for the eigenvalue -2, and a description of the eigenspace for -2 in generalized line graphs.
Most graphs that are known to be DS are either small, so that the property can be proved by complete enumeration, or they have a high degree of regularity.
Several graph invariants based on the spectra of matrices associated with the graph, with the property that they are minor monotone, will be presented and compared.
www.ma.hw.ac.uk /icms/current/graph/sci_prog.html   (1011 words)

  
 Norman Biggs - Research
Graph Theory 1736-1936 (with E.K. Lloyd and R.J. Wilson).
A trivalent graph with girth 9 and 58 vertices (with M. Hoare).
Algebraic methods for chromatic polynomials (with M H Klin and P Reinfeld).
www.maths.lse.ac.uk /Personal/norman/Research.htm   (962 words)

  
 Amazon.com: Modern Graph Theory: Books   (Site not responding. Last check: 2007-11-05)
The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole.
This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics.
Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest.
www.amazon.com /exec/obidos/tg/detail/-/0387984887?v=glance   (1196 words)

  
 The Math Forum - Math Library - Graph Theory   (Site not responding. Last check: 2007-11-05)
A graph is a set V of vertices and a set E of edges - pairs of elements of V. This simple definition makes Graph Theory the appropriate language for discussing (binary) relations on sets.
A series of short interactive tutorials introducing the basic concepts of graph theory, designed with the needs of future high school teachers in mind and currently being used in math courses at the University of Tennessee at Martin.
Students use algebraic methods to explore, model, and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning used in solving these problems.
mathforum.org /library/topics/graph_theory   (2425 words)

  
 Spectral Graph Theory   (Site not responding. Last check: 2007-11-05)
The underlying graph itself is introduced in a natural way by a move set (mutation operator, search strategy) on the set of possible configurations or genes.
The correlation functions are in turn uniquely determined by the geometry of the underlying configuration space and the nearest neighbor correlation of the elementary landscape.
We conclude that the algebraic approach to fitness landscape analysis can be extended to recombination spaces and provides an effective way to analyze the relative hardness of a landscape for a given recombination operator.
non.fiction.org /~await/alife/talks/maley/nov11-96.html   (415 words)

  
 Algebraic Graph Theory   (Site not responding. Last check: 2007-11-05)
Book Description: Algebraic graph theory is a fascinating subject concerned with the interplay between algebra and graph theory.
Algebraic tools can be used to give surprising and elegant proofs of graph theoretic facts, and there are many interesting algebraic objects associated with graphs.
His main research interests lie in the interactions between algebra and combinatorics, in particular the application of algebraic techniques to graphs, designs and codes.
isbn.nu /0387952411   (612 words)

  
 Algebraic Graph Theory - Computing Science and Mathematics, University of Stirling
The context for work in these areas is the relationship between the structure of a network graph and its algebraic invariants, which include the eigenvalues of an adjacency matrix.
A workshop on Algebraic Graph Theory at the International Centre for Mathematical Sciences, Edinburgh in July 1993.
A EuroWorkshop on Algebraic Graph Theory at the International Centre for Mathematical Sciences, Edinburgh in July 2001.
www.cs.stir.ac.uk /research/groups/alg-graph.html   (423 words)

  
 MATH285 Page   (Site not responding. Last check: 2007-11-05)
This course is concerned with the use of matrix techniques in the study of graphs.
The aim is to translate properties of graphs into matrix properties and then, using the results and methods of matrix, to deduce theorems about graphs.
B. Liu and H. Lai, Matrices in Combinatorics and Graph Theory, Kluwer 2000.
www.math.sjsu.edu /~so/math285.html   (136 words)

  
 Cayley graph   (Site not responding. Last check: 2007-11-05)
on two generators a and b In mathematics, a Cayley graph, named after Arthur Cayley, is a graph theory that encodes the structure of a group (mathematics).
It is a central tool in combinatorial group theory and geometric group theory.
Insights into the structure of the group can be obtained by studying the adjacency matrix of the graph and in particular applying the theorems of spectral graph theory.
read-and-go.hopto.org /Graphs/Cayley-graph.html   (242 words)

  
 Directory - Science: Math: Combinatorics: Graph Theory: People
Bela Bollobas  · cached · Functional analysis, combinatorics and graph theory.
Hubert de Fraysseix  · cached · Topological graph theory and combinatorics.
Graph Theory White Pages  · cached · Directory of graph theorists maintained by Daniel P. Sanders.
www.incywincy.com /default?p=415621   (119 words)

  
 Graph Theory Books   (Site not responding. Last check: 2007-11-05)
Graph Theory and its Applications by Gross.JL and Yellen.J CRC Press LLC, 1998
The Foundations of Topological Graph Theory by Bonnington.CP and Little.CHC Springer Verlag 1996
Distance-Regular Graphs by Brouwer.AE, A.M. Cohen, and A. Neumaier Springer-Verlag 1980
www1.cs.columbia.edu /~sanders/graphtheory/writings/books.html   (376 words)

  
 Joseph Malkevitch's Graph Theory Bibliography
Bodendiek, R., and R. Henn, Topics in Combinatorics and Graph Theory, Essays in Honor of Gerhard Ringel, Springer-Verlag, New York, 1990.
Capobianco, M., and M. Guan, D. Hsu, F. Tian (eds.), Graph Theory and Its Applications: East and West, Annals of the New York Academy of Sciences, Volume 576, New York Academy of Sciences, New York, 1989.
King, R., and D.j Rouvray, (eds.), Graph Theory and Topology in Chemistry, Studies in Physical and Theoretical Chemistry 51, Elsevier, New York, 1987.
www.york.cuny.edu /~malk/biblio/graph-theory-biblio.html   (1318 words)

  
 Amazon.com: Spectral Graph Theory (CBMS Regional Conference Series in Mathematics, No. 92) (Cbms Regional Conference ...   (Site not responding. Last check: 2007-11-05)
Algebraic Graph Theory (Cambridge Mathematical Library) by Norman Biggs
Graph Theory (Graduate Texts in Mathematics) by Reinhard Diestel
Beautifully written and elegantly presented, this book is based on 10 lectures given at the CBMS workshop on spectral graph theory in June 1994 at Fresno State University.
www.amazon.com /exec/obidos/tg/detail/-/0821803158?v=glance   (557 words)

  
 The Graph Theorists' Home Page Guide
First of all, if you're a graph theorist or some person with strong interest in graph theory (you need not to be a mathematician!), and if you have a homepage but don't find a link to it on this page, please contact me as described above.
PIGALE is a graph editor with an interface to the LEDA library and with many algorithms implemented essentially concerning planar graphs.
Methods are from the geometric side of algebraic topology and from the algebra of permutation groups.
www.joergzuther.de /math/graph/homes.html   (8696 words)

  
 Gallileus - Algebraic Graph Theory   (Site not responding. Last check: 2007-11-05)
Algebraic graph theory is a combination of two strands.
The second is the use of tools from algebra to derive properties of graphs.
TOC:Graphs.- Groups.- Transitive Graphs.- Arc-Transitive Graphs.- Generalized Polygons and Moore Graphs.- Homomorphisms.- Kneser Graphs.- Matrix Theory.- Interlacing.- Strongly Regular Graphs.- Two-Graphs.- Line Graphs and Eigenvalues.- The Laplacian of a Graph.- Cuts and Flows.- The Rank Polynomial.- Knots.- Knots and Eulerian Cycles.- Glossary of Symbols.- Index.
www.gallileus.info /search/lob_detail?isbn=0387952411   (217 words)

  
 GraphTheory   (Site not responding. Last check: 2007-11-05)
Graph Theory MAT 4399B/5301 / MATH 5801 - Winter 2005
To pass the Comprehensive Exam in Graph Theory, students must get a mark of 70% or higher on the final exam.
Students who register in MAT 4399B (undergraduate course) will be writing an easier version of the assignments and exams but can not get credit for a comprehensive exam.
www.mathstat.uottawa.ca /~msajn339/mat5301/main.html   (420 words)

  
 MATH 620 Algebraic Graph Theory Homepage   (Site not responding. Last check: 2007-11-05)
All of you must have taken a course in Abstract Algebra and Linear Algebra, some of you might have taken a course in Graph Theory and Combinatorics.
A basic course in abstract algebra and linear algebra is assumed.
It is strongly recommended that you keep some basic graph theory, linear algebra and abstract algebra books handy for reference.
courses.csusm.edu /math620rr   (418 words)

  
 Open Directory - Science: Math: Combinatorics: Graph Theory: Open Problems   (Site not responding. Last check: 2007-11-05)
Graph Coloring Problems - Archive for the book "Graph Coloring Problems" by Tommy R. Jensen and Bjarne Toft (Wiley Interscience 1995), dedicated to Paul Erdös.
Graph Theory Open Problems - Six problems suitable for undergraduate research projects.
Problems in Topological Graph Theory - Web text by Dan Archdeacon with a list of open questions in topological graph theory.
dmoz.org /Science/Math/Combinatorics/Graph_Theory/Open_Problems   (261 words)

  
 Algebraic Graph Theory - Cambridge University Press   (Site not responding. Last check: 2007-11-05)
Professor Biggs’ basic aim remains to express properties of graphs in algebraic terms, then to deduce theorems about them.
In the first part, he tackles the applications of linear algebra and matrix theory to the study of graphs; algebraic constructions such as adjacency matrix and the incidence matrix and their applications are discussed in depth.
There follows an extensive account of the theory of chromatic polynomials, a subject which has strong links with the ‘interaction models’ studied in theoretical physics, and the theory of knots.
www.cup.cam.ac.uk /catalogue/print.asp?isbn=0521458978&print=y   (235 words)

  
 Denis Simakov. Algebraic Graph Theory (Spring 2001)   (Site not responding. Last check: 2007-11-05)
Graphs and their spectra (adjacency algebra and spectrum of a graph, Perron-Frobenius theory, interlacing properties, invariant subspaces of an adjacency algebra).
Coherent (cellular) algebras (centraliser algebras, coherent algebras, Weisfeiler-Leman stabilization, various particular cases of a coherent algebra, graph isomorphism problem).
Prerequisites: Dicrete mathematics, linear algebra, elements of abstract algebra.
www.wisdom.weizmann.ac.il /~deniss/courses/spr01_klin.html   (198 words)

  
 Advanced Graph Theory at the University of Zimbabwe   (Site not responding. Last check: 2007-11-05)
We delve deeper into many areas first encountered in HMTH215 (Graph Theory) and look closely at many different areas and proofs in the literature.
Algebraic graph theory including distance regular and distance transitive graphs.
N L Biggs, Algebraic Graph Theory, (Cambridge, 1993).
www.uz.ac.zw /science/maths/courses/hmth340.htm   (100 words)

  
 Algebraic Graph Theory (Cambridge Mathematical Library): Current Amazon U.S.A. One-Edition Data
In the first section, he tackles the applications of linear algebra and matrix theory to the study of graphs; algebraic constructions such as adjacency matrix and the incidence matrix and their applications are discussed in depth.
There follows an extensive account of the theory of chromatic polynomials, a subject that has strong links with the "interaction models" studied in theoretical physics, and the theory of knots.
Here there are important connections with other branches of algebraic combinatorics and group theory.
www.negative-procreative.biz /stuff-0521458978.html   (348 words)

  
 Home page for: Algebraic Graph Theory   (Site not responding. Last check: 2007-11-05)
Brendan McKay - some very useful programs, eulerian graphs, trees, strongly regular graphs....
Gordon Royle - cubic and strongly regular graphs, biplanes,...
Chris Godsil: Algebraic Combinatorics, Chapman and Hall, New York, 1993.
quoll.uwaterloo.ca /agt   (93 words)

  
 A Simple Method for Constructing Small Cubic Graphs of Girths 14, 15, and 16 (ResearchIndex)   (Site not responding. Last check: 2007-11-05)
Abstract: A method for constructing cubic graphs with girths in the range 13 to 16 is described.
The method is used to construct the smallest known cubic graphs for girths 14, 15 and 16.
Biggs book on Algebraic Graph Theory [1] provides an introduction to this subject.
citeseer.ist.psu.edu /34417.html   (267 words)

  
 Courses Combinatorics and Optimization
Problems are taken mainly from the elementary parts of algebra, geometry, number theory, combinatorics and probability.
Topics may include planar graphs, extremal graph theory, directed graphs, enumeration, algebraic graph theory, probabilistic graph theory, connectivity, graph embedding, colouring problems.
Introduction to the theory of valid inequalities and polyhedral combinatorics.
www.adm.uwaterloo.ca /infoucal/COURSE/course-CO.html   (1617 words)

  
 math285
West, Introduction to Graph Theory, Prentince Hall, 1996.
Godsil and G. Royle, Algebraic Graph Theory, Springer 2001.
Liu and H. Lai, Matrices in Combinatorics and Graph Theory, Kluwer 2000.
www.sjsu.edu /faculty/wso/math285.htm   (112 words)

  
 CSE 365, Fall 2004   (Site not responding. Last check: 2007-11-05)
Midterm quiz: We will have a short midterm quiz on Monday, November 1st; it will not cover algebraic graph theory.
My presentation of algebraic graph theory roughly followed the discussion appearing in section 9, part 2 of "The Probabilistic Method," by Noga Alon and Joel Spencer.
The book has been recalled at the library and will be on reserve for the remainder of the semester.
www.engr.uconn.edu /~acr/Courses/cse365-fa04   (212 words)

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