21. Graph Theory 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. http://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.

22. A Constructive Approach To Graph Theory Notes on a semiotic approach to constructing isomorphism invariants of graphs by John-Tagore Tevet. http://www.hot.ee/tewet/

www.hot.ee/tewet has now been moved to www.graphs.ee

23. Graph Theory Graph Theory (Math 224) I am in Reiss 258. See my index page for office hours and contact information. For background info see course mechanics . http://www.georgetown.edu/faculty/kainen/graphtheory.html

Graph Theory (Math 224) I am in Reiss 258. See my index page for office hours and contact information. For background info see course mechanics New: schedule for midterms et al. The text is "Introduction to Graph Theory" by Richard J. Trudeau, which is in paperback from Dover Publications, NY, 1994; still in print and available in the bookstore or from amazon.com - here is a picture I've got a page with some basic material on graph theory here . You can also find definitions (not always the same!) for various graph-theoretic terms, and even tutorials, on the web. Back to the classroom page Dec. 11, 2005 As I told you by e-mail, there are practice problems on top of the file cabinet just to the left of my office door in Reiss 258. When you've tried these, you may want to look over the answers to the practice problems For the graph theory final (Reiss 281, Monday Dec. 12 at 9 = 11 am) be prepared to demonstrate your knowledge of graph theory. I won't expect anything too tricky in the nature of a proof. You should be familiar with the basic concepts without worrying about regurgitating definitions. I realize that one can get confused trying to recall the distinction between, say, book thickness and genus - but if you are briefly reminded what it means and then given a concrete example, I would expect that you can then work out, say, the Euler lower bound. If you are seeing concepts and theorems for the first time, it is quite difficult to use them correctly. On the other hand, if you have reviewed these topics before, then they should be easy to apply in concrete cases.

24. SGT - Spectral Graph Theory People, publications, research topics, open problems, events and resources. http://www.sgt.pep.ufrj.br/

var pagina = "index.php"; The theory of graph spectra can, in a way, be considered as an attempt to utilize linear algebra including, in particular, the well-developed theory of matrices for the purposes of graph theory and its applications. However, that does not mean that the theory of graph spectra can be reduced to the theory of matrices; on the contrary, it has its own characteristic features and specific ways of reasoning that fully justifying it to be treated as a theory in its own right. It has the curious feature that some of the main results, although purely combinatorial in character, seem in the present state of knowledge to be unobtainable without resorting to algebraic methods involving a consideration of eigenvalues of adjacency matrices of graphs. There are unexplored and semi-explored territories in graph theory. It will be apparent that the results achieved so far barely scratch the surface of what appears to be a rich area of investigation. CARIOCA GRAPH a split nonthreshold Laplacian integral graph.

25. Graph Theory SpringerVerlag, Heidelberg Graduate Texts in Mathematics, Volume 173 ISBN 978-3-642-14278-9 July 2010 (2005, 2000, 1997) 451 pages; 125 figures http://diestel-graph-theory.com/index.html

26. Graph Theory -- From Eric Weisstein's Encyclopedia Of Scientific Books Eric Weisstein's Encyclopedia of Scientific Books see also Combinatorics, FourColor Problem, Graph Theory. Avondo Bodino, Giuseppe. http://www.ericweisstein.com/encyclopedias/books/GraphTheory.html

Graph Theory see also Combinatorics Four-Color Problem Graph Theory Avondo Bodino, Giuseppe. Economic Applications of the Theory of Graphs. New York: Gordon and Breach, Science Publishers, 1962. 111 p. $?. Beinecke, Lowell Wayne and Wilson, Robin James (Eds.). Graph Connections: Relationships Between Graph Theory and Other Areas of Mathematics. Oxford, England: Oxford University Press, 1997. 304 p. $65. Berge, Claude. Graphs and Hypergraphs, 2nd rev. ed. Amsterdam, Netherlands: North-Holland, 1976. 528 p. $138. Berge, Claude. Hypergraphs: The Theory of Finite Sets. Amsterdam, Netherlands: North-Holland, 1989. 255 p. $?. Berge, Claude. The Theory of Graphs and Its Applications. New York: Wiley, 1962. 247 p. $?. Biggs, Norman L. Algebraic Graph Theory, 2nd ed. Cambridge, England: Cambridge University Press, 1993. 205 p. $26.95. Biggs, Norman L.; Lloyd, E. Keith; and Wilson, Robin J. Graph Theory 1736-1936. Oxford, England: Oxford University Press, 1976. $45. Graph Theory: An Introductory Course. New York: Springer-Verlag, 1979. 180 p. $43.50. Modern Graph Theory.

27. Graph Theory And Linear Algebra Unreviewed paper by Stephen M Kauffman. http://www.bcpl.net/~smkauffm/gtlawatersigned.pdf

28. Ideas, Concepts, And Definitions 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 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 . . .

29.  An Overview On Graph Theory Definitions and classical problems. 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)

30. Graph Theory And Its Applications -- About The Authors: Jonathan Gross Graph Theory and Its Applications About the Authors Jonathan Gross http://www.graphtheory.com/gross.htm

o Home Page o About the Authors o Jonathan L. Gross o Jay Yellen o ORDER THE BOOKS o Graph Theory Resources o People o Research o Writings o Conferences o Journals o The Four-Color o Theorem o White Pages o White Pages ....o Registration o Combinatorial Methods Toolkit NEW o Feedback o Site Correction Change Request o Errata in GTAIA 2 ed o Request an Evaluation Copy o Graphsong Last Edited 13 Sep 2009 Aaron D. Gross Email the Webmaster Graph Theory Textbooks and Resources About the Authors Professor Jonathan L. Gross Jonathan L. Gross is Professor of Computer Science at Columbia University. His research in topology, graph theory, and cultural sociometry has earned him an Alfred P. Sloan Fellowship, an IBM Postdoctoral Fellowship, and various research grants from the Office of Naval Research, the National Science Foundation, and the Russell Sage Foundation. Professor Gross has created and delivered numerous software- development short courses for Bell Laboratories and for IBM. These include mathematical methods for performance evaluation at the advanced level and for developing reusable software at a basic level. He has received several awards for outstanding teaching at Columbia University, including the career Great Teacher Award from the Society of Columbia Graduates. He appears on the Columbia Video Network and on the video network of the National Technological University.

31. Math Cove Contents With the software Petersen written by C. Mawata. http://www.utc.edu/Faculty/Christopher-Mawata/

Teaching and Learning Mathematics with Java Math Cove Projects Rigid Transformations High School Geometry Graph Theory Lessons Trominos ... Awards since 4/22/98

32. 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: This is an old site. The current work is at http://www.mathcove.net/petersen/ 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 Phone: 423-755-4545 fax: 423-755-4586 e-mail: C. Mawata

33. Graph Theory Article For Social Measurement Graph Theory Stephen C. Locke Department of Mathematical Sciences Florida Atlantic University. Outline. Abstract Glossary History Notation Algorithms Some Elegant Theorems http://math.fau.edu/locke/SocialMeasurement/Article.htm

Graph Theory Stephen C. Locke Department of Mathematical Sciences Florida Atlantic University Outline Abstract Glossary History Notation Algorithms Some Elegant Theorems Unsolved Problems Suggested Reading References Abstract A graph can be thought of as a representation of a relationship on a given set. For example, the set might be the set of people in some town, and the relationship between two people might be that they share a grandparent. Graph Theory is the study of properties of graphs. In particular, if the graph is known to have one property, what other properties must it possess? Can one find certain features of the graph in a reasonable amount of time? In this article, we mention a few of the more common properties, some theorems relating these properties, and refer to some methods for finding structures within a graph. Glossary algorithm : A procedure for solving a problem. bipartite : A graph whose vertices fall into two classes; for example, if the vertices represent men and women. cycle : A route, using at least one edge, which returns to its starting point, but does not repeat any vertex except for the first and the last.

34. Recommended Courses In Discrete Mathematics | Crux Sancti Patris Benedicti Course descriptions for Graph Theory and related topics by Philip Pennance. http://pennance.us/home/courses/dm.php

Crux Sancti Patris Benedicti Recommended Courses in Discrete Mathematics Graph Theory I Discrete Algorithms Computers and Intractability. Theory of NP-completeness. Enumerative Combinatorics I ... MATH 8001 Graph Theory I. Three credits. Three hours of lecture per week. Prerequisites: MATH 5CCC (Graph Theory). Justification It is difficult to overestimate the importance of graph theory in contemporary mathematics and its applications. Deep and elegant in itself, graph theory contains many wonderful ideas and results. Methods and ideas of graph theory are widely used in many other areas of mathematics. Graph theory has a tremendous number of applications. It would not be an exaggeration to say that graph theory is one of the most applicable areas of mathematics. It serves as a theoretical basis for a great variety of applied areas such as computer science, operations research, management science, electrical and mechanical engineering, chemistry, biology, etc. This course will be useful to the students who are planning to pursue doctoral studies in mathematics and its applications. Objectives This course will furnish the student with an excellent basis for study and research in a wide variety of mathematical areas. It will provide the student with skills which will be of use in mathematics and in various applications.

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

Graph Theory Resources Graph Theory Resources

36. Wolf, Goat, Cabbage Introduction to basic graph theory, using a puzzle and its generalizations. http://www.eprisner.de/WZK/WZK1.html

Erich Prisner Wolf, goat, cabbage, ... Difficulty Level 1: You want to transfer wolf ("W"), goat ("G"), and cabbage ("C") from the left bank of the river to the right bank. You, the only human there, are the rower, and don't leave the boat. The wolf wants to eat the goat, the goat wants to eat the cabbage, but nothing will happen as long as you are near. Beside you there is only place for one item in the boat. How can you achieve your task? Click on "W", "G", or "C" to put them in or out of the boat. Click the boat to get it moving. Unfortunately your browser does not support Java applets. In this puzzle you can hardly do anything wrong as long as you obey the rule Never do something to get a situation you had already before. The only possible first move is to ship the goat, "G", to the right. Shipping it back would violate our rule, therefore we go back with an empty boat. We may not go empty to the right (we would violate the rule). therefore we take "W" or "C", which one really doesn't matter, the situation is symmetric, so let's say "W" moves. Now we have to take something back, but not "W" (remember our rule), so we ship "G" to the left. Next we ship "C" to the right. Here is the only state where you could do something wrong by shipping "W" to the left-instead we row with an empty boat to the left, pick up "G", and ship to the right. Variants: More items to move The puzzle being so simple, one might ask: Can we change it to make it more complicated? What happens if we have to move a school class? You can formulate the instance of your problem in the

37. Graph (mathematics) - Wikipedia, The Free Encyclopedia Most commonly, in modern texts in graph theory, unless stated otherwise, graph means undirected simple finite graph (see the definitions below). http://en.wikipedia.org/wiki/Graph_(mathematics)

Graph (mathematics) From Wikipedia, the free encyclopedia Jump to: navigation search For the graph of a function, see Graph of a function Further information: Graph theory A drawing of a labeled graph on 6 vertices and 7 edges. In mathematics , a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices , and the links that connect some pairs of vertices are called edges . Typically, a graph is depicted in diagrammatic form as a set of dots for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics The edges may be directed (asymmetric) or undirected (symmetric). For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this is an undirected graph, because if person A shook hands with person B, then person B also shook hands with person A. On the other hand, if the vertices represent people at a party, and there is an edge from person A to person B when person A knows of person B, then this graph is directed, because knowing of someone is not necessarily a symmetric relation (that is, one person knowing of another person does not necessarily imply the reverse; for example, many fans may know of a

38. 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.

39. Graph Theory -- From Wolfram MathWorld The mathematical study of the properties of the formal mathematical structures called graphs. http://mathworld.wolfram.com/GraphTheory.html

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Interactive Demonstrations 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 ... Walk 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. New 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.

40. Problems In Graph Theory Maintained by Peter Cameron. http://www.maths.qmw.ac.uk/~pjc/oldprob.html

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