1. Graph Theory graph theory. If you have a graph theory page, let me know and I might includea link to it from my page for links to other people s files. http://www.math.fau.edu/locke/graphthe.htm

Graph Theory You can contact Stephen C. Locke at LockeS@fau.edu 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.

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

Graph Theory Lessons 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 Index: Links To Definitions Project Director: Dr. Christopher P. Mawata Department of Mathematics University of Tennessee at Chattanooga 615 McCallie Avenue Chattanooga, TN 37403-2598 Phone: 423-755-4545 fax: 423-755-4586 e-mail: C. Mawata This page has been hit times since April 8, 1997.

3. Other Graph Theory And Related Pages Miscellaneous pages collected by Stephen C. Locke. http://www.math.fau.edu/locke/graphoth.htm

Other Graph Theory and Related Pages If you want me to add a link to your Combinatorics Page, contact Stephen C. Locke at LockeS@fau.edu . I make no promises about any of the pages you might get to from here. These are pages written by other people. As always, if you run across something you don't like, hit the back button. My Index Graph Theory Pages http://www.graphtheory.com/resources.htm Gary Chartrand Ibrahim Cahit Chuck Lindsey ... clindsey@fgcu.edu at Florida Gulf Coast University. Some Lecture Notes from MAD 5305. Graph Theory Tutorial . Ran across this and this first page looked nice. Had some trouble that some links didn't work. Might try it out later. Chris Mawata cmawata@cecasun.utc.edu University of Tennessee at Chattanooga. Some lessons. , communicated to me by Martin Laenger Knight's Tour material by Mark R. Keen If you are looking for algorithms, I don't know of very many sources. Don't forget to look at the maple software. It can calculate tutte polynomials , for example. I presume Mathematica also has software. The following list was sent to me by David Eppstein eppstein@euclid.ICS.UCI.EDU

4. Graph Theory Glossary graph theory Glossary. Chris Caldwell © 1995. This glossary is writtento supplement the Interactive Tutorials in graph theory. http://www.utm.edu/departments/math/graph/glossary.html

Graph Theory Glossary Chris Caldwell This glossary is written to supplement the Interactive Tutorials in Graph Theory . Here we define the terms that we introduce in our tutorialsyou may need to go to the library to find the definitions of more advanced terms. Please let me know of any corrections or suggestion! A B C D ... Z adjacent Two vertices are adjacent if they are connected by an edge. arc A synonym for edge. See graph articulation point See cut vertices bipartite A graph is bipartite if its vertices can be partitioned into two disjoint subsets U and V such that each edge connects a vertex from U to one from V. A bipartite graph is a complete bipartite graph if every vertex in U is connected to every vertex in V. If U has n elements and V has m , then we denote the resulting complete bipartite graph by K n,m . The illustration shows K . See also complete graph and cut vertices chromatic number The chromatic number of a graph is the least number of colors it takes to color its vertices so that adjacent vertices have different colors. For example, this graph has chromatic number three. When applied to a map this is the least number of colors so necessary that countries that share nontrivial borders (borders consisting of more than single points) have different colors. See the

5. Graph Theory graph theory resources www.graphtheory.com graph theory. Resources. maintained by Daniel P The Four Color Theorem. graph theory White Pages Search http://www.cs.columbia.edu/~sanders/graphtheory

6. The Graph Theory White Pages Translate this page The graph theory White Pages. maintained by Daniel P. Sanders as partof www.graphtheory.com Resources People Research Writings The http://www.cs.columbia.edu/~sanders/graphtheory/people/alphabetic.html

7. Ideas, Concepts, And Definitions 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. 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 . . .

8. 05C: Graph Theory This simple definition makes graph theory the appropriate language for discussing (binary) relations on sets, which 05C10 Topological graph theory, imbedding, See also 57M15, 57M25 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.)

9. Electronic Version Reinhard Diestel. graph theory. Second Edition. Electronic Edition.Here is a complete electronic edition of the book, which you are http://www.math.uni-hamburg.de/home/diestel/books/graph.theory/download.html

Reinhard Diestel Graph Theory Second Edition Electronic Edition Here is a complete electronic edition of the book, which you are welcome to view or download to your computer for offline use. It comes as a hyperlinked pdf file; click here for some hints on how to download and view pdf files. View/download the electronic edition from this site now, or download it by anonymous ftp from ftp://ftp.math.uni-hamburg.de/pub/unihh/math/books/diestel/GraphTheoryII.pdf (login: "anonymous", password: your email address). Return to main page

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

11. Software On Graph Theory Free Software for Win 9X,NT on graph theory by Vitali Petchenkine. Procedures Metrics of the graph; Paths and cycles; Colorations; Automorphism group; Minimal spanning tree; Shortest paths; Max. Capacity path; K Shortest paths; Salesman problem; Maximal flow; Critical path; Reports for Graphs; Print. http://www.geocities.com/pechv_ru/

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12. Graph Theory Tutorials graph theory Tutorials. This is the home page for a series of short interactivetutorials introducing the basic concepts of graph theory. 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. [

13. Graph Theory And Constraint Programming University course definitions, lecture notes, books, language descriptions, links. http://www.cs.adfa.edu.au/~gtc/GTC/

Graph Theory and Constraint Programming The 1998 notes are available here Table of Contents General Course Information Some related web pointers Lectures Course Software ... rim@cs.adfa.edu.au Last Modified: 27 June 2000 jcmunro@bigpond.com

14. Graph Theory Tutorials graph theory Tutorials This site includes Introduction to graph theory, Euler Circuits and Paths, Coloring Problems, and Adjacency Matrices (under construction). Each section consists of an http://rdre1.inktomi.com/click?u=http://www.utm.edu/departments/math/graph/&

15. 17th Cmberland Conference Combinatorics, graph theory and Computing. Middle Tennessee State University, Murfreesboro, TN, USA; 2022 May 2004. http://www.mtsu.edu/~sseo/Cumberland17.htm

The 17th Cumberland Conference on Combinatorics, Graph Theory, and Computing May 20 to May 22, 2004 Thursday, May 20 1:00 pm - 5:30 pm Friday, May 21 8:00 am - 5:30 pm Saturday, May 22 8:00 am - 11:30 am Principal Speakers Organizing Committee Invited Speakers/Abstracts Schedule ... Parking Info Conference Aim The Cumberland Conference on Graph Theory, Combinatorics and Computing is an annual meeting of the discrete mathematics community in the southeast. The Conference brings together internationally known researchers, college faculty, students, industrial mathematicians, and computer scientists in an environment conducive to the interchange of ideas and leading to opportunities for collaborative research. Everyone is welcome to attend. As there is no registration fee, the Cumberland Conference is a convenient opportunity for students and faculty, especially those from smaller institutions, to meet and interact with others who are interested and active in research in various areas of discrete mathematics.

16. Combinatorics And Graph Theory With Mathematica Combinatorica is a library of 230 functions turning Mathematica into a powerful tool for graph theory and combinatorics. http://www.combinatorica.com/

17. DCCG Workshop, Lethbridge, July 2001 Second Lethbridge Workshop on Designs, Codes, Cryptography and graph theory a combination of instructional lectures and research sessions. Lethbridge, Alberta; July 914, 2001. http://www.cs.uleth.ca/dccg/

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18. Games On Graphs Overview. Graphs are mathematical objects that are made of dots connected by lines.graph theory is the branch of mathematics that involves the study of graphs. http://www.c3.lanl.gov/mega-math/workbk/graph/graph.html

Overview Graphs are mathematical objects that are made of dots connected by lines. Graph Theory is the branch of mathematics that involves the study of graphs. Graphs are very powerful tools for creating mathematical models of a wide variety of situations. Graph theory has been instrumental for analyzing and solving problems in areas as diverse as computer network design, urban planning, and molecular biology. Graph theory has been used to find the best way to route and schedule airplanes and invent a secret code that no one can crack. The Big Picture

19. Discussiones Mathematicae Graph Theory Contents, abstracts from vol.15 (1995). Full text of some articles. http://www.pz.zgora.pl/discuss/gt/

Discussiones Mathematicae Graph Theory Discussiones Mathematicae Graph Theory

20. Graph Theory Lesson 8 graph theory Lessons. graphic graphic graphicLesson 8 Graph Coloring.Get the graph of a cube (it is under the Platonic Graph menu item). http://www.utc.edu/~cpmawata/petersen/lesson8.htm

Graph Theory Lessons Lesson 8: Graph Coloring Get the graph of a cube (it is under the Platonic Graph menu item). Click Properties and Chromatic number . What this does is to color the vertices of the graph using as few colors as possible and making sure that adjacent vertices always have different colors. We shall call such a coloring a proper coloring. The cube, for example, can be properly colored using just two colors. Fig. 11, A properly colored cube. The number of colors used is called the chromatic number of the graph. We use X(G) to denote the chromatic number of the graph G In the applet below draw a few graphs on the left side. The applet will display a proper coloring of the graph you draw. Use the program to find the chromatic number of each of the five platonic graphs. Use the program to find the chromatic number of the complete graphs K , K , K From part 2, what do you think the chromatic number of K n is? Use the program to find the chromatic number of the Petersen graph. If a graph G is a subgraph of G what can you say about X(G and X(G If a graph contains a triangle (a subgraph isomorphic to K ) what is the smallest chromatic number it can have?

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