1. Graph Theory - Wikipedia, The Free Encyclopedia In mathematics and computer science, graph theory is the study of graphs; mathematical structures used to model pairwise relations between objects from a http://en.wikipedia.org/wiki/Graph_theory

Graph theory From Wikipedia, the free encyclopedia Jump to: navigation search A drawing of a graph. In mathematics and computer science graph theory is the study of graphs ; mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of vertices. A graph may be undirected , meaning that there is no distinction between the two vertices associated with each edge, or its edges may be directed from one vertex to another; see graph (mathematics) for more detailed definitions and for other variations in the types of graphs that are commonly considered. The graphs studied in graph theory should not be confused with " graphs of functions " and other kinds of graphs Contents History Drawing graphs Graph-theoretic data structures List structures ... edit History The K¶nigsberg Bridge problem. The paper written by Leonhard Euler on the Seven Bridges of K¶nigsberg and published in is regarded as the first paper in the history of graph theory . This paper, as well as the one written by

2. Graph Theory Tutorials Basic concepts of graph theory by Chris Caldwell. http://www.utm.edu/departments/math/graph/

Graph Theory Tutorials Chris K. Caldwell (C) 1995 This is the home page for a series of short interactive tutorials introducing the basic concepts of graph theory. There is not a great deal of theory here, we will just teach you enough to wet your appetite for more! Most of the pages of this tutorial require that you pass a quiz before continuing to the next page. So the system can keep track of your progress you will need to register for each of these courses by pressing the [REGISTER] button on the bottom of the first page of each tutorial. (You can use the same username and password for each tutorial, but you will need to register separately for each course.) Introduction to Graph Theory (6 pages) Starting with three motivating problems, this tutorial introduces the definition of graph along with the related terms: vertex (or node), edge (or arc), loop, degree, adjacent, path, circuit, planar, connected and component. [ Suggested prerequisites: none Euler Circuits and Paths Suggested prerequisites: Introduction to Graph Theory Coloring Problems (6 pages) How many colors does it take to color a map so that no two countries that share a common border have the same color? This question can be changed to "how many colors does it take to color a planar graph?" In this tutorial we explain how to change the map to a graph and then how to answer the question for a graph. [

3. Graph Theory By Reinhard Diestel. Sites offers author and book information as well as a downloadable PDF version of the book. http://www.math.uni-hamburg.de/home/diestel/books/graph.theory/

Reinhard Diestel Graph Theory Third Edition Springer-Verlag, Heidelberg Graduate Texts in Mathematics, Volume 173 Hardcover US$89.95, EUR69,95 ISBN 3-540-26182-6 Softcover US$49.95, EUR39,95 ISBN 3-540-26183-4 July 2005 (2000, 1997) 431 pages; 146 figures About the Book: Reviews About the author Overview: Summary, blurb: edition Preface: edition Contents Electronic Edition and Errata: There is a free, searchable, and hyperlinked electronic edition , which may be downloaded for offline use. Errata: edition How to Order: Individual copies and course adoptions (discount plus free desk copy) German Edition Further Reading Home

4. Graph Theory Definitions of graph theory terms. http://www.math.fau.edu/locke/GRAPHTHE.HTM

Graph Theory How to contact me Why I don't want to talk about: Goldbach's Conjecture Index Brief History Basic Definitions If you have a graph theory page, let me know and I might include a link to it from my page for links to other people's files . I won't usually link to commercial pages. Please note also: I have received requests for assistance on problems that are standard undergraduate exercises. The most I will do in these situations is point out the exercise in a standard text (in case the writer doesn't realize that it is a standard problem) or refer the writer to a chapter in a standard textbook. Very Brief History The earliest paper on graph theory seems to be by Leonhard Euler, Solutio problematis ad geometriam situs pertinentis, Commetarii Academiae Scientiarum Imperialis Petropolitanae 8 (1736), 128-140. Euler discusses whether or not it is possible to stroll around Konigsberg (later called Kaliningrad) crossing each of its bridges across the Pregel (later called the Pregolya) exactly once. Euler gave the conditions which are necessary to permit such a stroll. Thomas Pennyngton Kirkman (1856) and William Rowan Hamilton (1856) studied trips which visited certain sites exactly once.

5. Graph Theory graph theory resources www.graphtheory.com. graph theory Resources. http://www1.cs.columbia.edu/~sanders/graphtheory/

Graph Theory Resources Graph Theory Resources

6. Ideas, Concepts, And Definitions In the branch of mathematics called graph theory, a graph bears no Graph paper is not particularly useful for drawing the graphs of graph theory. http://www.c3.lanl.gov/mega-math/gloss/graph/gr.html

Graphs and Graph Theory In the branch of mathematics called Graph Theory, a graph bears no relation to the graphs that chart data, such as the progress of the stock market or the growing population of the planet. Graph paper is not particularly useful for drawing the graphs of Graph Theory. In Graph Theory, a graph is a collection of dots that may or may not be connected to each other by lines. It doesn't matter how big the dots are, how long the lines are, or whether the lines are straight, curved, or squiggly. The "dots" don't even have to be round! All that matters is which dots are connected by which lines. Two dots can only be connected by one line. If two dots are connected by a line, it's not "legal" to draw another line connecting them, even if that line stretches far away from the first one. If you look at a graph and your eyes want to zip all around it like a car on a race course, or if you notice shapes and patterns inside other shapes and patterns, then you are looking at the graph the way a graph theorist does. Here are some of the special words graph theorists use to describe what they see when they are looking at graphs: edge vertex degree size ... dominating set See also . . .

7. Graph Theory Lessons A set of graph theory lessons (undergraduate level) that go with the software Petersen written by C. Mawata. http://www.utc.edu/~cpmawata/petersen/

Graph Theory Lessons Note: If your browser can handle java2 applets, then you should use the site I am keeping current at http://www.utc.edu/Faculty/Christopher-Mawata/petersen2/index.htm About the program Petersen Quick Directions Extra Credit Problem! Lesson 1: Null graphs Lesson 2: Handshaking Lemma Lesson 3: Isomorphism Lesson 4: Complete Graphs, Subgraphs Lesson 5: Regular Graphs Lesson 6: Platonic Graphs Lesson 7: Adjacency Matrices Lesson 8: Graph Coloring Lesson 9: Bipartite Graphs Lesson 10: Stars and Tripartite Graphs Lesson 11: Circuits and Wheels Lesson 12: Euler Circuits, Hamilton Circuits and Directed Graphs Lesson 13: Trees and Searches Lesson 14: Unions and Sums Lesson 15: Complements Lesson 16: Prisms Lesson 17: Laces Lesson 18: Line Graphs Lesson 19: Grids Lesson 20: Spanning Trees Lesson 21: Planar Graphs Lesson 22: Dual Graphs Lesson 23: Weighted Graphs, Shortest Paths, and Minimal Spanning Trees Project Director: Dr. Christopher P. Mawata Department of Mathematics University of Tennessee at Chattanooga 615 McCallie Avenue Chattanooga, TN 37403-2598

8. Graph Theory -- From Wolfram MathWorld Graph Connections Relationships Between graph theory and Other Areas of Mathematics. Oxford, England Oxford University Press, 1997. http://mathworld.wolfram.com/GraphTheory.html

Search Site Algebra Applied Mathematics Calculus and Analysis ... General Graph Theory Graph Theory The mathematical study of the properties of the formal mathematical structures called graphs SEE ALSO: Adjacency Matrix Adjacency Relation Algorithmic Graph Theory Articulation Vertex ... [Pages Linking Here] REFERENCES: Ahmad, M. A. "Muhammad Aurangzeb Ahmad's Encyclopedia of Graph Theory." http://www.cs.rit.edu/~maa2454/Graphs/ Beinecke, L. W. and Wilson, R. J. (Eds.). Graph Connections: Relationships Between Graph Theory and Other Areas of Mathematics. Oxford, England: Oxford University Press, 1997. Berge, C. Graphs and Hypergraphs. Ney York: Elsevier, 1973. Berge, C. The Theory of Graphs and Its Applications. New York: Wiley, 1962. Bogomolny, A. "Graphs." http://www.cut-the-knot.org/do_you_know/graphs.shtml Graph Theory: An Introductory Course. New York: Springer-Verlag, 1979. Modern Graph Theory. New York: Springer-Verlag, 1998. Caldwell, C. K. "Graph Theory Tutorials." http://www.utm.edu/departments/math/graph/ Chartrand, G. Introductory Graph Theory.

9. Graph Theory graph theory is a 2005 commission of the New Radio and Performing Arts, Inc., (aka Ether Ore) for its Turbulence web site. It http://www.turbulence.org/Works/graphtheory/

Graph Theory is a 2005 commission of the New Radio and Performing Arts, Inc., (aka Ether Ore) for its Turbulence web site. It was made possible with funding from the Greenwall Foundation. Jason Freeman : concept, music, programming Patricia Reed : design Maja Cerar : violin click to launch (If you have disabled JavaScript on your web browser, click here instead.)

10. Wiley InterScience :: JOURNALS :: Journal Of Graph Theory Devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete http://www.interscience.wiley.com/jpages/0364-9024/

Skip to Content If you are seeing this message, you may be experiencing temporary network problems. Please wait a few minutes and refresh the page. If the problem persists, you may wish to report it to your local Network Manager. It is also possible that your web browser is not configured or not able to display style sheets. In this case, although the visual presentation will be degraded, the site should continue to be functional. We recommend using the latest version of Microsoft or Mozilla web browser to help minimise these problems. Wiley InterScience HOME ABOUT US CONTACT US ... HELP JOURNALS Home Mathematics and Statistics Mathematics (general) Journal of Graph Theory See Also: Journal of Graph Theory 1977-1995 What is RSS? Get Sample Copy Recommend to Your Librarian ... Print this page Journal Home Product Information Editorial Board For Authors Subscribe ... Contact Issue Navigation Early View Current Issue ALL ISSUES (1996 - 2008) Previous Issue Next Issue Current Issue Volume 57 Issue 1 (January 2008) A note on complete subdivisions in digraphs of large outdegree (p 1-6) Published Online: Oct 22 2007 12:12PM DOI: 10.1002/jgt.20255

11. 05C: Graph Theory Classified in the MSC as a subfield of 05 Combinatorics, graph theory has emerged as a related but largely independent discipline. 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.)

12. Graph Theory With Applications graph theory with Applications. Main page. graph theory with Applications. J.A. Bondy and U.S.R. Murty. The complete book (270 pages). Individual chapters http://www.ecp6.jussieu.fr/pageperso/bondy/books/gtwa/gtwa.html

Main page Graph Theory with Applications J.A. Bondy and U.S.R. Murty The complete book (270 pages) Individual chapters: Preface Contents Chapter 1: Graphs and Subgraphs Chapter 2: Trees Chapter 3: Connectivity Chapter 4: Euler Tours and Hamilton Cycles Chapter 5: Matchings Chapter 6: Edge Colourings Chapter 7: Independent Sets and Cliques Chapter 8: Vertex Colourings Chapter 9: Planar Graphs Chapter 10: Directed Graphs Chapter 11: Networks Chapter 12: The Cycle Space and Bond Space Appendix 1: Hints to Starred Exercises Appendix II: Four Graphs and a Table of their Properties Appendix III: Some Interesting Graphs Appendix IV: Unsolved Problems Appendix V: Suggestions for Further Reading Glossary of Symbols Index Free counter

13. Algorithmic Graph Theory graph theory Links, graph theory Lecture Notes, graph theory Journals, bibilography etc. http://www.personal.kent.edu/~rmuhamma/GraphTheory/graphTheory.htm

Algorithms Compilers Computer Architecture Computational Geometry ... Parallel Computing Graph Theory Lecture Notes Introduction Definitions and Examples Eulerian Graphs Hamiltonian Graphs ... Graph Coloring Related Links Advanced Topics in Graph Algorithms (ps) by Ron Shamir Technical report based on lecture notes. Collection of Lecture Notes, Surveys, and Papers at U. of Paderborn-Germany C ompendium of NP optimization problems, A Edited by Pierluigi Crescenzi and Viggo Kann Continuously updated catalog of approximability results for NP optimization problems Geometry in Action: Graph Drawing by David Eppstein, U. California-Irvine Graphs and Graph Theory Graph Coloring Page Graph Drawing Tutorial (pdf) by Isabel F. Cruz and Roberto Tamassia Graph Theory (pdf) byReinhard Diestel Free searchable and hyperlinked electronic edition of the book. Graph: Theory - Algorithms - Complexity Graph Theory Tutorials and Graph Theory Glossary Graph Theory and its Applications comprehensive graph theory resource for graph theoreticians and students. Graph Theory White Pages, The

14. Graph Theory graph theory. graph theory. graph theory. Covering and Partitioning MINIMUM VERTEX COVER MINIMUM DOMINATING SET MAXIMUM DOMATIC PARTITION http://www.ensta.fr/~diam/ro/online/viggo_wwwcompendium/node8.html

Next: Covering and Partitioning Up: A compendium of NP Previous: Improving the compendium Index Graph Theory Graph Theory Covering and Partitioning M INIMUM V ... NFERENCE Viggo Kann

15. Graph Theory Information about researchers in graph theory and their papers. http://www.math.gatech.edu/~sanders/graphtheory/

Graph Theory Resources maintained by Daniel P. Sanders People Research Writings ... Graph Theory White Pages Search new at Graph Theory Resources The database of papers has now been updated through April 10, 2007 It is possible to search for any graph theorist, regardless if I have contact information for him. This does not mean that I am not actively collecting graph theorist contact information. Please keep that information coming. Please try out the two links below: Graph Theory White Pages Search Graph Theory White Pages Geographic Search Translations German: Graphentheorie Betriebsmittel French: Italian: Teoria Dei Grafi - Risorse Spanish: This page was the AEI December, 1997, Mathematics of Computing Cool Site

16. ``Introduction To Graph Theory'' (2nd Edition) It is easy to invent terminology in graph theory, but independently invented terminology is unlikely to agree. Here I solicit your votes on five questions 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 the third edition) Solution manual - available to instructors only : to get the solution manual, go to www.prenhall.com, search for this book by title or ISBN, click on "instructor" on the page for the book, fill out the requested information identifying you as an instructor, and wait for email with instructions for accessing the solution manual. Syllabus for a one-semester beginning course (used at U Illinois) postscript pdf 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.)

17.  An Overview On Graph Theory The famous problem of the bridges of Königsberg, solved by Euler, is viewed as the first formal result in graph theory. This theory has developed during the http://www-leibniz.imag.fr/GRAPH/english/overview.html

Leibniz Laboratory, The Graph Theory Team Home Members References Our topics ... Our software An overview on Graph Theory A graph is a very simple structure consisting of a set of vertices and a family of lines (possibly oriented), called edges (undirected) or arcs (directed), each of them linking some pair of vertices. An undirected graph may for example model conflicts between objects or persons. A directed graph (or digraph) may typically represent a communication network , or some domination relation between individuals, etc. The famous problem of the The number of concepts that can be defined on graphs is very large, and many generate deep problems or famous conjectures (for instance the four colour problem ). In fact, many of these concepts or theoretical questions arise from practical reasons (and not just from the mathematicians' imaginations) for solving real problems modeled on graphs. Moreover, researchers in Graph Theory try if possible to find efficient algorithms for solving these problems. The main classical problems in Graph Theory are : flow and connectivity (network reliability)

18. Group 8 - Graph Theory Tutorial One of the first people to experiment with graph theory was a man by the name of Leonhard Euler (17071783). He attempted to solve the problem of crossing http://www.cs.usask.ca/resources/tutorials/csconcepts/1999_8/

Please select one of the above frames. "menu" is a menu to choose from three sections of the tutorial. "content" is the body of the menu item you choose.

19. 05Cxx 05C05 Trees; 05C07 Degree sequences; 05C10 Topological graph theory, imbedding See also 57M15, 57M25; 05C12 Distance in graphs; 05C15 Coloring of graphs http://www.ams.org/msc/05Cxx.html

Home MathSciNet Journals Books ... Contact Us 201 Charles Street Providence, RI 02904 USA Phone: 401-455-4000 or 800-321-4AMS Or email us at ams@ams.org Open Positions Graph theory 05C05 Trees 05C07 Degree sequences 05C10 Topological graph theory, imbedding [See also 05C12 Distance in graphs 05C15 Coloring of graphs and hypergraphs 05C17 Perfect graphs 05C20 Directed graphs (digraphs), tournaments 05C22 Signed, gain and biased graphs 05C25 Graphs and groups [See also 05C30 Enumeration of graphs and maps 05C35 Extremal problems [See also 05C38 Paths and cycles [See also 05C40 Connectivity 05C45 Eulerian and Hamiltonian graphs 05C50 Graphs and matrices 05C55 Generalized Ramsey theory 05C60 Isomorphism problems (reconstruction conjecture, etc.) 05C62 Graph representations (geometric and intersection representations, etc.) 05C65 Hypergraphs 05C69 Dominating sets, independent sets, cliques 05C70 Factorization, matching, covering and packing 05C75 Structural characterization of types of graphs 05C78 Graph labelling (graceful graphs, bandwidth, etc.) 05C80 Random graphs 05C83 Graph minors 05C85 Graph algorithms [See also 05C90 Applications 05C99 None of the above, but in this section

20. Graph Theory Open Problems Six problems suitable for undergraduate research projects. http://dimacs.rutgers.edu/~hochberg/undopen/graphtheory/graphtheory.html

Graph Theory Open Problems Index of Problems Unit Distance Graphs-chromatic number Unit Distance Graphs-girth Barnette's Conjecture Crossing Number of K(7,7) ... Square of an Oriented Graph Unit Distance Graphs-chromatic number RESEARCHER: Robert Hochberg OFFICE: CoRE 414 Email: hochberg@dimacs.rutgers.edu DESCRIPTION: How many colors are needed so that if each point in the plane is assigned one of the colors, no two points which are exactly distance 1 apart will be assigned the same color? This problem has been open since 1956. It is known that the answer is either 4, 5, 6 or 7-this is not too hard to show. You should try it now in order to get a flavor for what this problem is really asking. This number is also called ``the chromatic number of the plane.'' A graph which can be embedded in the plane so that vertices correspond to points in the plane and edges correspond to unit-length line segments is called a ``unit-distance graph.'' The question above is equivalent to asking what the chromatic number of unit-distance graphs can be. Here are some warm-up questions, whose answers are known: What complete bipartite graphs are unit-distance graphs? What's the smallest 4-chromatic unit-distance graph? Show that the Petersen graph is a unit-distance graph.

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