41. The Graph Theory Team Leibniz Laboratory, The graph theory Team. get acquainted with the membersof the graph theory team;; take a look at our overview on graph theory;; http://www-leibniz.imag.fr/GRAPH/english/welcome.html

Leibniz Laboratory, The Graph Theory Team Members Overview References Our topics ... Our software This is the home page of the graph theory team of the Leibniz Laboratory (part of the IMAG Institute , Grenoble, France). From here you can: get acquainted with the members of the graph theory team take a look at our overview on Graph Theory look up a list of general references on Graph Theory; peek at our research topics see the software developed by some member(s) of the team. Winter school : New Methods in Discrete Mathematics Thanks for your visit!

42. 05C: Graph Theory Introduction. Yes, a longer introduction to graph theory will eventuallyappear . Classified in the MSC as a subfield of 05 Combinatorics http://www.math.niu.edu/~rusin/known-math/index/05CXX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 05C: Graph theory Introduction [Yes, a longer introduction to graph theory will eventually appear...] Classified in the MSC as a subfield of 05: Combinatorics , Graph Theory has emerged as a related but largely independent discipline. A graph History See e.g. Wilson, Robin J.: "200 years of graph theory-a guided tour" Theory and applications of graphs (Proc. Internat. Conf., Western Mich. Univ., Kalamazoo, Mich., 1976), pp. 19. Lecture Notes in Math., Vol. 642, Springer, Berlin, 1978. MR58 #15981. A longer version appeared in book form: Biggs, Norman L.; Lloyd, E. Keith; Wilson, Robin J.: "Graph theory: 17361936" Clarendon Press, Oxford, 1976. 239 pp. MR56#2771 Applications and related fields Particularly regular graphs are related to Group Theory . This includes discussion of automorphism groups, Cayley diagrams for groups, and regular graphs. Many graph-theoretic problems can be solved by exhaustive enumeration; the questions then involve complexity. Further topics in this area are included in 68: Computer Science . (In particular this area of overlap includes topics such as the Traveling Salesman Problem, treated here.)

43. Home Page For: Algebraic Graph Theory Algebraic graph theory. The book Publisher Springer Verlag (New York). RelatedTexts. Reinhard Diestel graph theory (Springer 1997). http://quoll.uwaterloo.ca/agt/

Algebraic Graph Theory The book: Publisher: Springer Verlag (New York). ISBN: 0-387-95220-9 A postcript copy of the preface and table of contents is here. The authors: Gordon Royle and Chris Godsil Order it online: At amazon.com Supplementary material Extensions to material in the text here. Known errors (and some fixes) Here. On-line data and programs Brendan McKay - some very useful programs, eulerian graphs, trees, strongly regular graphs.... Gordon Royle - cubic and strongly regular graphs, biplanes,... Ted Spence - 2-designs, Hadamard matrices, two-graphs,.... Markus Meringer's regular graphs Related Texts Reinhard Diestel: Graph Theory (Springer 1997). Bollobas: Modern Graph Theory. West: Introduction to Graph Theory. Biggs: Algebraic Graph Theory. Chris Godsil: Algebraic Combinatorics, Chapman and Hall, New York, 1993. (ISBN: 0-412-04131-6) To Contact Us by mail: or electr(on)ically: email: cgodsil@math.uwaterloo.ca tel: (519) 888 4567 X5593 fax: (519) 725 5441 Last modified: Mon Jul 30 09:57:17 EDT 2001

44. American Scientist: Computing Science: January-February 2000 graph theory in Practice Part I. The diameter in question is not a geometric distance;the concept comes from the branch of mathematics called graph theory. http://www.sigmaxi.org/amsci/issues/comsci00/compsci2000-01.html

January-February 2000 Computing Science Graph Theory in Practice: Part I Brian Hayes Note: This document is available in other formats What is the diameter of the World Wide Web? The answer is not et al. Connect the Dots The graphs studied by graph theorists have nothing to do with the wiggly-line charts that plot stock prices. Here is a definition of a graph, in all its glory of abstraction: A graph is a pair of sets, V and E , where every element of E is a two-member set whose members are elements of V . For example, this is a graph: V a b c E a b a c So much for definitions; most of us prefer to think of our graphs graphically. And in fact everyone knows that what graph theory is really about is connecting the dots. The set V is made up of vertices (also known as nodes), which are drawn as dots. The set E consists of edges (also called arcs, links or bonds), and each edge is drawn as a line joining the two vertices at its end points. Thus the graph defined abstractly above looks like this: Euler showed that you can answer the question by tabulating the degree or valency The techniques of graph theory soon proved useful for more than planning a stroll along the Pregel. The German physicist Gustav Kirchoff analyzed electric circuits in terms of graphs, with wires as edges and junction points as vertices. Chemists found a natural correspondence between graphs and the structural diagrams of molecules: An atom is a vertex, and an edge is a bond between atoms. Graphs also describe communications and transportation networks, and even the neural networks of the brain. Other applications are less obvious. For example, a chess tournament is a graph: The players are nodes, and matches are edges. An economy is also a graph: Companies or industries are nodes, and edges represent transactions.

45. American Scientist: Computing Science: March-April 2000 graph theory in Practice Part II. Brian Hayes. But graph theory is a branch of mathematicsthat has never been afraid to get its hands dirty with applications. http://www.sigmaxi.org/amsci/issues/comsci00/compsci2000-03.html

March-April 2000 March-April, Volume 88, No. 2 Computing Science Graph Theory in Practice: Part II Brian Hayes Note: This document is available in other formats Part I of this article, in the January-February issue, discussed some very large structures that can usefully be looked upon as mathematical graphs. In this context a graph is a set of vertices (which are usually represented as dots) and a set of edges (lines between the dots). One large object that can be described in this way is the World Wide Web; its 800 million pages are the vertices of a graph, and links from one page to another are the edges. A second example comes out of Hollywood: The vertices are 225,000 actors, and an edge connects any two actors who have appeared in a feature film together. Although graph theory has a history of two centuries and more, only in recent years has it been applied routinely to structures like these, with many thousands or millions of vertices and edges. Studying such enormous graphs is by no means easy. The Hollywood collaboration graph just barely fits in the memory of a large computer. The Web, a few orders of magnitude larger, requires all the resources of the Internet to keep track of its tentacles. Certain other graphs are even bigger. The human acquaintanceship graph, with a vertex for every person on earth and edges linking all those who know each other, may never be recorded beyond a few small, sampled regions. The Small World of Large Graphs The various gigantic graphs that have lately attracted notice share other properties besides sheer size. In particular:

46. ``Introduction To Graph Theory'' (2nd Edition) Introduction to graph theory Second edition. This is the home pagefor Introduction to graph theory, by Douglas B. West. Published http://www.math.uiuc.edu/~west/igt/

Introduction to Graph Theory - Second edition This is the home page for Introduction to Graph Theory , by Douglas B. West Published by Prentice Hall 1996, 2001. Second edition, xx+588 pages, 1296 exercises, 447 figures, ISBN 0-13-014400-2. First edition 512+xvi pages, 870 exercises, 312 figures, ISBN 0-13-227828-6. Resources Supplementary Exercises not yet in text (to be added in later editions) Solution manual - available to instructors only from george_lobell@prenhall.com Syllabus for a one-semester beginning course (postscript) (used at U Illinois) Contents and Preface for second edition (postscript) Errata for second edition Corrections to notation and to other mathematical aspects Comments and updates (corrections to references, comments on proofs or exercises, etc.) Minor typos (errors in spelling, punctuation, etc.) Resources for first edition (no longer maintained): Errata Syllabus Contents and Preface Reader Poll on Terminology (Now Three Questions!) Terminology is a big problem in graph theory: it is easy to invent terminology, and independently invented terminology is unlikely to agree. Here is your opportunity to vote on terminology. I will try to honor the vote in the third edition. Please send email to west@math.uiuc.edu

47. A CONSTRUCTIVE APPROACH TO GRAPH THEORY Notes on a semiotic approach to constructing isomorphism invariants of graphs by JohnTagore Tevet.Category Science Math Combinatorics graph theory......A CONSTRUCTIVE APPROACH TO graph theory. Title. General.Results. Complementary data. In German. In Russian. http://hot.ee/tewet/

A CONSTRUCTIVE APPROACH TO GRAPH THEORY Title General Results Complementary data ... In Russian

48. Algebraic Graph Theory Home Page The general theme is the geometric representation of graphs and on this occasion the chosen area of Category Science Math graph theory Events Past Conferences......EuroWorkshop on Algebraic graph theory. Edinburgh 913 July 2001. http://www.ma.hw.ac.uk/icms/current/graph/

EuroWorkshop on Algebraic Graph Theory Edinburgh 9-13 July 2001 Workshop Arrangements Scientific Programme Participants List Call for Papers ... Click here for the report on this meeting in ICMS News 11 Timetable available on Scientific Programme page Scientific Committee D. Cvetkovic (Belgrade) W. Haemers (Tilburg) P. Rowlinson (Stirling). The general themeof this second workshop on Algebraic Graph Theory is the geometric representation of graphs and on this occasion the chosen area of application is discrete mathematical chemistry. The workshop provides an opportunity for the scattered communities of algebraic graph theorists and mathematical chemists to discuss recent developments of mutual interest. The main topics are seen as the new fullerenes eigenspace techniques generalizations from distance-regular graphs topological considerations In addition to formally timetabled lectures, there will be ample time for more informal discussion. Most days will begin and end with a lecture from a key speaker, with contributed short papers (20-25 minutes) timetabled in between (using two parallel sessions if necessary to avoid saturation). The meeting is supported by The European Commission (Framework V) The London Mathematical Society The British Combinatorial Committee This meeting's pages last updated 05 July 2001 Future Events Travel Information Call for Proposals Publications ... Front Page

49. Graph Theory Of Brian Alspach - Simon Fraser Univ. - 2003 Simon Fraser University, Burnaby, BC, Canada; 2529 May 2003.Category Science Math Combinatorics graph theory Events...... http://www.cs.uleth.ca/gtba/

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50. Fourth Cracow Conference On Graph Theory "Czorsztyn '02" Czorsztyn, Poland; 1620 September 2002.Category Science Math graph theory Events Past Conferences...... of Applied Mathematics University of Mining and Metallurgy in Cracow has organizedFOURTH CRACOW CONFERENCE ON graph theory CZORSZTYN '02 Czorsztyn, Poland http://galaxy.uci.agh.edu.pl/~graphs/

Faculty of Applied Mathematics University of Mining and Metallurgy in Cracow has organized FOURTH CRACOW CONFERENCE ON GRAPH THEORY "CZORSZTYN '02" Czorsztyn, Poland September 16-20, 2002 Deadline for submission of papers to the special issue of Discrete Mathematics is October 31, 2002. If you want to contribute to that volume please send us electronically either .ps or .pdf file as well as three hardcopies of your paper. Conference photos are available in two resolution/quality modes: medium quality (files of aprrox. 700 KB size) high quality (files of aprrox. 2 MB size) e-mail: graphs@uci.agh.edu.pl www: http://galaxy.uci.agh.edu.pl/~graphs phone: ++48 12 617 3582 fax: ++48 12 617 3165 mailing address: Faculty of Applied Mathematics, University of Mining and Metallurgy al. Mickiewicza 30, 30-059 Kraków, Poland

51. Graph Theory Of Brian Alspach - Simon Fraser Univ. - 2003 http://www.cs.uleth.ca/~holzmann/gtba/

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52. The Math Forum - Math Library - Graph Theory This page contains sites relating to graph theory. Browse and Searchthe Library Home Math Topics Discrete Math graph theory. http://mathforum.org/library/topics/graph_theory/

Browse and Search the Library Home Math Topics Discrete Math : Graph Theory Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites (see also All Sites in this category This problem inspired the great Swiss mathematician Leonard Euler to create graph theory, which led to the development of topology. more>> The Four Colour Theorem - MacTutor Math History Archives Linked essay describing work on the theorem from its posing in 1852 through its solution in 1976, with two other web sites and 9 references (books/articles). more>> Graph Theory - Dave Rusin; The Mathematical Atlas more>> Graph Theory Tutorials - Chris K. Caldwell 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. An Introduction to Graph Theory tutorial uses three motivating problems to introduce the definition of graph along with terms like vertex, arc, degree, and planar. Includes a glossary and a partially annotated bibliography of graph theory terms and resources. Euler Circuits and Paths; Coloring Problems (Maps). more>> Unsolved problems on perfect graphs, a collection for people with at least a basic knowledge of the subject. Contents include: Perfection of special classes of Berge graphs; Recognition of special classes of Berge graphs; Decompositions of perfect graphs; Minimal imperfect graphs, partitionable graphs, and monsters; Parity problems; The P4-structure; Quantitative variations on the Strong Perfect Graph Conjecture; Intersection graphs; The Markosyan manoeuvre; Appendix: Odds and ends. With a bibliography, and home pages of people interested in perfect graphs.

53. Graph Theory graph theory. Introduction. Note here that a more emotive phrase for the multinationaltax planning problem is tax avoidance . graph theory example 1995 UG exam. http://www.ms.ic.ac.uk/jeb/or/graph.html

OR-Notes J E Beasley OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). They were originally used by me in an introductory OR course I give at Imperial College. They are now available for use by any students and teachers interested in OR subject to the following conditions A full list of the topics available in OR-Notes can be found here Graph theory Introduction Graph theory deals with problems that have a graph (or network) structure. In this context a graph (or network as many people use the terms interchangeable) consists of: vertices/nodes - which are a collection of points; and arcs - which are lines running between the nodes. Such arcs may be directed or undirected and undirected arcs are often called links or edges. An example graph is shown below. Graph theory is used in dealing with problems which have a fairly natural graph/network structure, for example: road networks - nodes = towns/road junctions, arcs = roads communication networks - telephone systems computer systems foreign exchange/multinational tax planning (network of fiscal flows) Note here that the minimum cost network flow problem (also dealt with in this course) is an example of a problem with a graph/network structure.

54. Introductory Graph Theory This book has been written by G. Chartrand with several objectives in mind to teach the reader some Category Science Math Combinatorics graph theory Books......Introductory graph theory. By Gary Chartrand Western Michigan University Networksas Mathematical Models. Chapter 2 Elementary Concepts of graph theory. http://www.wmich.edu/math-stat/people/faculty/chartrand/introgt/

Introductory Graph Theory By Gary Chartrand Western Michigan University Published by Dover Paperbacks About the Book Table of Contents Chapter 1: Mathematical Models Nonmathematical Models Mathematical Models Graphs Graphs as Mathematical Models Directed Graphs as Mathematical Models Networks as Mathematical Models Chapter 2: Elementary Concepts of Graph Theory The Degree of a Vertex Isomorphic Graphs Connected Graphs Cut-Vertices and Bridges Chapter 3: Transportation Problems The Konigsberg Bridge Problem: An Introduction to Eulerian Graphs The Salesman's Problem: An Introduction to Hamiltonian Grpahs Chapter 4: Connection Problems The Minimal Connector Problem: An Introduction to Trees Trees and Probability PERT and the Critical Path Method Chapter 5: Party Problems The Problem of Eccentric Hosts: An Introduction to Ramsey Numbers The Dancing Problem: An Introduction to Matching Chapter 6: Games and Puzzles The Problem of the Four Multicolored Cubes: A Solution to "Instant Insanity" The Knight's Tour The Tower of Hanoi The Three Cannibals and Three Missionaries Problem Chapter 7: Digraphs and Mathematical Models A Traffic System Problem: An Introduction to Orientable Graphs Tournaments Paired Comparisons and How to Fix Elections Chapter 8: Graphs and Social Psychology The Problem of Balance The Problem of Clustering Graphs and Transactional Analysis Chapter 9: Planar Graphs and Coloring Problems The Three Houses and Three Utilities Problem: An Introduction to Planar Graphs

55. OUP USA: ToC: Graph Theory As I Have Known It graph theory As I Have Known It WT Tutte CONTENTS. 1. Squaring thesquare 2. Knights errant 3. Graphs within graphs 4. Unsymmetrical http://www.oup-usa.org/toc/tc_0198502516.html

Graph Theory As I Have Known It W. T. Tutte CONTENTS 1. Squaring the square 2. Knights errant 3. Graphs within graphs 4. Unsymmetrical electricity 5. Algebra in graph theory 6. Symmetry in graphs 7. Graphs on spheres 8. The cats of Cheshire 9. Reconstruction 10. Planar enumeration 11. The chromatic eigenvalues 12. In conclusion References Index General Catalog Information Publication dates and prices are subject to change without notice. Prices are stated in US Dollars and valid only for sales transacted through the US website. Please note: some publications for sale at this website may not be available for purchase outside of the US. This page last updated Thursday, 13-Mar-2003 15:33:46 EST Please send comments or suggestions about this server to webmaster@oup-usa.org

56. OUP USA: ToC: Graph Theory 1736-1936 Two centuries of graph theory, by Norman L. Biggs, E. Keith Lloyd, and Robin J. Wilson.Category Science Math Combinatorics graph theory Books......graph theory 17361936 Norman L. Biggs, E. Keith Lloyd, and Robin J.Wilson CONTENTS. 1. Paths 2. Circuits 3. Trees 4. Chemical Graphs http://www.oup-usa.org/toc/tc_0198539169.html

Graph Theory 1736-1936 Norman L. Biggs, E. Keith Lloyd, and Robin J. Wilson CONTENTS 1. Paths 2. Circuits 3. Trees 4. Chemical Graphs 5. Euler's Polyhedral Formula 6. The Four-Colour ProblemEarly History 7. Colouring Maps on Surfaces 8. Ideas from Algebra and Topology 9. The Four-Colour Problemto 1936 10. The Factorization of Graphs Appendix 1: Graph Theory since 1936 Appendix 2: Bibliographical Notes Appendix 3: Bibliography: 1736-1936 Index of Names General Catalog Information Publication dates and prices are subject to change without notice. Prices are stated in US Dollars and valid only for sales transacted through the US website. Please note: some publications for sale at this website may not be available for purchase outside of the US. This page last updated Thursday, 13-Mar-2003 15:33:59 EST Please send comments or suggestions about this server to webmaster@oup-usa.org

57. The Graph Theorists' Home Page Guide Links to home pages of graph theorists maintained by Jorg Zuther.Category Science Math Combinatorics graph theory People...... If you don't want a listby-name, there's also a search engine graph theory WhitePages Search; 12.12.1999 I want to add that I'm no longer in graph theory. http://www.math.tu-berlin.de/~zuther/math/graph/homes.html

The Graph Theorists' Home Page Guide TU Berlin Dept. Mathematics Page Index Home ... Legend Index of this Page News What do you find on this page? Why do I maintain this page? You're a graph theorist and want to see your name here? ... Z Links on this page have last been checked: May 30th, 2002 Last update: February 22nd, 2003 News : Link rot has become a great annoyance. The usefulness of this page is strongly reduced because of this problem. See the page " Cool URIs don't change " of the for a description and many tips to avoid this problem. : I must apologize to some people who had to wait very long to be put onto this page (some more than one year!!). My time was very tight and I had big problems in updating the page. I have to apologize even more since I didn't answer some mails and have even lost some. I'm ***VERY*** sorry about that! So, if you have tried to contact me but received no answer and still don't find your name here, please try again. I beg your pardon. This time, I promise to do it within one week. : I plan to use an XML approach to maintain my web pages. This will cost a lot of time but will pay off when it comes to put new data onto the pages or changing the layout. Further, I'm thinking about some improvements of the data: I want to include email (and people who have only email but no homepage) and the

58. Jörg Zuther's Underworld Of Graph Theory And Combinatorics Note page is under construction. Jörg Zuther'sUnderworld of graph theory and Combinatorics. http://www.math.tu-berlin.de/~zuther/math/graph/

Note: page is under construction TU Berlin Dept. Mathematics Group Page Index ... Maths Graph Theory Games Words Sites Features The Graph Theorists' Home Page Guide >100k !!, more than 200 people Searching for the address of a certain graph theorist? Want to know what he's doing? Want to get a preprint from him? Maybe you can find a link to his home page on this list... Combinatorial and Graph Theoratical Journals (under construction) Combinatorial and Graph Theoretical Subject Pages (under construction) Combinatorial and Graph Theoretical Software (under construction) Algorithmische Graphentheorie (German) The author Volker Turau presents his book. TU Berlin Dept. Mathematics Group Page Index ... Maths Graph Theory Games Words Sites page established: 11.12.1997 Critics, comments, remarks, questions? Mail to last modified: 04.02.2000 zuther@math.tu-berlin.de

59. STORM: PhD Opportunities Research and courses in linear and additive models, queueing theory and reliability, combinatorial optimisation, graph theory, and the underrepresentation of working class students in Higher Education. http://www.unl.ac.uk/storm/

Studying at UNL International Students How to Apply Online Prospectus Open Days, Tours, Virtual Tour Accommodation Course Information Contact Us Studying at UNL International Students How to Apply Online Prospectus Open Days, Tours, Virtual Tour Accommodation Course Information Contact Us Course Information Services for Students International Students Uni Life Course Information Services for Students International Students Uni Life Welcome Virtual Tour Media Room Contact Us Welcome Virtual Tour Media Room Contact Us Research Office Research Institutes Business Links Postgraduate Study Contact Us Research Office Research Institutes Business Links Postgraduate Study Contact Us Human Resources Research Office Omnibus Purchasing Services Human Resources Research Office Omnibus Purchasing Services Alumni Association Stay Connected Fundraising Contact Us Alumni Association Stay Connected Fundraising Contact Us init(3); STORM: Statistics, Operational Research and Probabilistic Methods Research Centre Enquiries PhD Opportunities Research Short Courses ... Links STORM Home Page Home Schools and Faculties Science, Computing and Engineering

60. Graph Theory - Wikipedia Other languages Deutsch. graph theory. From Wikipedia, the free encyclopedia.graph theory problem. Glossary of basic graph theory concepts. 6n http://www.wikipedia.org/wiki/Graph_theory

Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help Other languages: Deutsch Polski Graph theory From Wikipedia, the free encyclopedia. Graph theory is the branch of mathematics that examines the properties of graphs A graph is a set of dots, called vertices or nodes, connected by links, called edges or arcs. Depending on the applications, edges may or may not have a direction; edges joining a vertex to itself may or may not be allowed, and vertices and/or edges may be assigned weights, i.e. numbers. If the edges have a direction associated with them (indicated by an arrow in the graphical representation) we have a directed graph Structures that can be represented as graphs are ubiquitous, and many problems of practical interest can be formulated as questions about certain graphs. For example directed graphs are used to represent finite state machines . The development of algorithms to compute certain properties of graphs is therefore of major interest in computer science Definitions of Graphs and Digraphs The basic definitions in graph theory vary in the literature. Here are the conventions used in this encyclopedia.

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