81. 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

82. 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.

83. 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.

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

Graph Theory Resources Graph Theory Resources

85. 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

86. 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

87. 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.

88. 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.

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

90. Dan Archdeacon's Home Page Topological graph theory, combinatorics, theoretical computer science. http://www.emba.uvm.edu/~archdeac/

91. What Is Graph Theory? Definition From WhatIs.com Graph theory is the study of points and lines. In particular, it involves the ways in which sets of points, called vertices, can be connected by lines or arcs, called edges. http://whatis.techtarget.com/definition/0,,sid9_gci934747,00.html

graph theory HOME SEARCH BROWSE BY CATEGORY BROWSE BY ALPHABET ... WHITE PAPERS Search our IT-specific encyclopedia for: Browse alphabetically: A B C D ... Hardware graph theory Graph theory is the study of points and lines. In particular, it involves the ways in which sets of points, called vertices, can be connected by lines or arcs, called edges. Graphs in this context differ from the more familiar coordinate plots that portray mathematical relations and functions. Graphs are classified according to their complexity, the number of edges allowed between any two vertices, and whether or not directions (for example, up or down) are assigned to edges. Various sets of rules result in specific properties that can be stated as theorems. Graph theory has proven useful in the design of integrated circuits ( IC s) for computers and other electronic devices. These components, more often called chip s, contain complex, layered microcircuits that can be represented as sets of points interconnected by lines or arcs. Using graph theory, engineers develop chips with maximum component density and minimum total interconnecting conductor length. This is important for optimizing processing speed and electrical efficiency. Last updated on: Sep 21, 2005

92. Stephen C. Locke Graph theory and algorithms. http://www.math.fau.edu/locke/

S.C. Locke Note : The mathematics server is now "math.fau.edu" rather than "www.math.fau.edu". If pages don't load, please snip the "www" from the URL. How to contact me Problem of the Week BA/BS Checkout Sheet (* add MAT 4937 *), BA Flow Chart BS Flow Chart Mathematics Introductory Sequences Sample 4-year schedule ... The national test (Grade 8) Background Information Professor, Department of Mathematical Sciences Florida Atlantic University Ph.D. in Combinatorics and Optimization University of Waterloo Ph.D. Supervisor: Professor J.A. Bondy Thesis title: Extremal Properties of Paths, Cycles and k-Colourable Subgraphs of Graphs Academic Family Tree , prepared by David Wood. M.Math. ( Combinatorics and Optimization University of Waterloo B.Math. ( Combinatorics and Optimization and Pure Mathematics University of Waterloo , 1975. Putnam competitor for all four years. Our team won in 1974. Married since 1974 to Joanne Thomson Locke B.Math. 1977, B.A. 1979, U.W. Sons Daniel , A.A. seeking at

93. Dr. Bela Bollobas Functional analysis, combinatorics and graph theory. http://www.msci.memphis.edu/faculty/bollobasb.html

Dr. Bela Bollobas Professor Hardin Chair of Excellence in Combinatorics D. Sc., Cambridge University, 1985 Ph.D., Cambridge University, 1972 Dr. Rer. Nat., Budapest, 1967 Department of Mathematical Sciences The University of Memphis Memphis, TN 38152-3240 Office: 243 Winfield Dunn Phone: (901) 678-5610 Fax: (901) 678-2480 email: bollobas@msci.memphis.edu Research interests: functional analysis and combinatorics. Mathematical Sciences Faculty Department of Mathematical Sciences

94. GRAPH-THEORY.LOVE.COM | All Things Graph Theory Research firm Gartner has published the latest update to its Hype Cycle for Emerging Technologies, which graphs the uptake of new products and inventions. http://graph-theory.love.com/

95. Rich Lundgren Applied graph theory and combinatorial matrix theory. http://www-math.cudenver.edu/~rlundgre/

96. Graph Theory » Bondy And Murty Entry Details. You’re currently reading “Bondy and Murty,” an entry on Graph Theory. Published January 12, 2008 around 12pm Category Photos Comments http://blogs.springer.com/bondyandmurty/?p=81

97. Gordon Royle Algebraic graph theory. http://www.csse.uwa.edu.au/~gordon/

Combinatorial Catalogues One of my main research interests is producing catalogues of interesting combinatorial objects, such as graphs, designs, geometries and so on. Graphs Small graphs Small multigraphs Cubic graphs Symmetric cubic graphs (Foster Census) ... Cubic Cages and higher valency cages Planar graphs Cubic Planar graphs (drawings!) Strongly regular graphs (parameters) ... Constructions of Certain Graphs Regular graphs (coming) Other goodies (coming) Geometries Projective planes of order 16 Translation planes of order 49 Translation planes (coming) Sets of type (m,n) (coming) Other goodies (coming) Designs Small designs Biplanes Groups Numbers of small groups Generators of small groups

98. Graph Theorists Directory of graph theorists maintained by Daniel P. Sanders. http://www1.cs.columbia.edu/~sanders/graphtheory/people/

Graph Theorists maintained by Daniel P. Sanders as part of www.graphtheory.com Resources People Research ... Graph Theorist Families Inter-Institution Groups GRAPHNET - e-mail discussion list DIMANET - The European Network On Discrete Mathematics DIMACS - center for DIscrete MAth and Computer Science (New Jersey, USA) EIDMA - Euler Institute for Discrete Mathematics and its Applications (Netherlands) CONE - Combinatorialists Of New England CMSA - Combinatorial Mathematics Society of Australasia (Inc.) ... ECC - East Coast Combinatorics (Canada) Rankings Most Journal Articles in Graph Theory Most Journal Article Pages in Graph Theory Most Journal Articles / Authors in Graph Theory Most Journal Article Pages / Authors in Graph Theory ... Breakdown By Olympiad Sources of Info on Graph Theorists The Graph Theorists' Home Page Guide (by J. Zuther Home pages of combinatorial people and groups (by N. Calkin

99. Graph Theory -- Britannica Online Encyclopedia graph theory, branch of mathematics concerned with networks of points connected by lines. The subject of graph theory had its beginnings in recreational math problems (see http://www.britannica.com/EBchecked/topic/242012/graph-theory

document.write(''); Search Site: Advanced Search With all of these words With the exact phrase With any of these words Without these words Home SHOP BROWSE BLOG ... HELP Username: Password: Remember me Forgot your password? Help Email " is the e-mail address you used when you registered. Password " is case sensitive. If you need additional assistance, please contact customer support Enter the e-mail address you used when enrolling for Britannica Premium Service and we will e-mail your password to you. graph-theory My Britannica CREATE MY graph theory NEW ARTICLE ... SAVE graph theory Table of Contents: graph theory Article Article Additional Reading Additional Reading Related Articles Related Articles Citations Article Additional Reading Related Articles Citations Primary Contributor: Stephan C. Carlson ARTICLE from the graph theory branch of mathematics concerned with networks of points connected by lines. The subject of graph theory had its beginnings in recreational math problems ( see number game ), but it has grown into a significant area of mathematical research with applications in chemistry operations research social sciences , and computer science The history of graph theory may be specifically traced to 1735, when the Swiss mathematician

100. Binh Minh Bui Xuan Graph theory, graph algorithms and computation. http://www.lirmm.fr/~buixuan/

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