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 certain collection. 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 Graphs are one of the prime objects of study in Discrete Mathematics . Refer to Glossary of graph theory for basic definitions in graph theory. Contents History Drawing graphs Graph-theoretic data structures List structures ... edit History The Königsberg Bridge problem The paper written by Leonhard Euler on the Seven Bridges of Königsberg and published in 1736 is regarded as the first paper in the history of graph theory.

2. Graph Theory - Encyclopedia Article - Citizendium This is a draft article, under development and not meant to be cited; you can help to improve it. These unapproved articles are subject to a disclaimer. http://en.citizendium.org/wiki/Graph_theory

Graph theory From Citizendium, the Citizens' Compendium Jump to: navigation search addthis_pub = 'citizendium'; addthis_logo = ''; addthis_logo_color = ''; addthis_logo_background = ''; addthis_brand = 'Citizendium'; addthis_options = ''; addthis_offset_top = ''; addthis_offset_left = ''; Main Article Talk Related Articles Bibliography External Links This is a draft article , under development and not meant to be cited; you can help to improve it. These unapproved articles are subject to edit intro Graph theory is the field of mathematics which deals with the study of graphs . A graph is defined as a set of vertices or nodes and edges or arcs which join the nodes. For example, the following graph has two nodes (labeled 'a' and 'b'), and a single arc joining them. Graphs have a wide variety of real-world applications. They are naturally well suited for expressing problems involving geographical information, but they can also be used for expressing far more abstract information such as possible strategies in a game theory question, or available courses of action for manipulating database tables. Types of Graphs There are certain specific types of graphs which express additional information and/or have certain restrictions applied to them. A few examples are listed here:

3. Graph Theory - Wiktionary The study of the properties of graphs (in the sense of sets of vertices and sets of ordered or unordered pairs of vertices). http://en.wiktionary.org/wiki/graph_theory

graph theory Definition from Wiktionary, the free dictionary Jump to: navigation search Contents English Noun Derived terms Translations ... edit English edit Noun Wikipedia has an article on: Graph theory Wikipedia graph theory ... mathematics The study of the properties of graphs (in the sense of sets of vertices and sets of ordered or unordered pairs of vertices). edit Derived terms graph-theoretical edit Translations study of networks of nodes and vertices Czech: teorie grafů cs (cs) f Danish: grafteori da (da) c Dutch: grafentheorie Esperanto: grafeteorio grafeiko teorio de grafeoj Finnish: graafiteoria fi (fi) French: théorie des graphes f German: Graphentheorie f Hebrew: he (he) f Hungarian: gráfelmélet hu (hu) Icelandic: netafræði f graffræði f Italian: teoria dei grafi f Japanese: (ぐらふりろん, gurafu-riron) Portuguese: teoria dos grafos f Russian: Spanish: teoría de los grafos f edit See also Appendix:Glossary of graph theory Retrieved from " http://en.wiktionary.org/wiki/graph_theory Categories Mathematics Graph theory Personal tools New features Log in / create account Namespaces Entry Discussion Variants Views Read Edit History Actions Search Navigation Main Page Community portal Preferences Requested entries ... Contact us Toolbox What links here Related changes Upload file Special pages ... Permanent link In other languages Français Svenska Tiếng Việt This page was last modified on 19 October 2010, at 07:33.

4. Graph Theory - Simple English Wikipedia, The Free Encyclopedia Graph theory is a field of mathematical ideas about graphs. A graph is an abstract representation A number of points are connected by lines. Each point is usually called http://simple.wikipedia.org/wiki/Graph_theory

Graph theory From Wikipedia, the free encyclopedia Jump to: navigation search An undirected graph. Graph theory is a field of mathematical ideas about graphs. A graph is an abstract representation: A number of points are connected by lines . Each point is usually called vertex (many are called vertices ), and the lines are called edges . Graphs are a tool for modelling. They are used to find answers to a number of problems. Some of these questions are: What is the best way for a mailman to get to all of the houses in the area in the least amount of time ? The points could represent street corners and lines could represent the houses along the street. (see Chinese postman problem A salesman has to visit different customers, but wants to keep the distance traveled as small as possible. The problem is to find a way so they can do it. This problem is known as Travelling Salesman Problem (and often abbreviated TSP ). It is among the hardest problems to solve. If a commonly believed conjecture is true (described as P NP ), then an exact solution requires one to try all possible routes to find which is shortest.

5. Graph Theory - Discussion And Encyclopedia Article. Who Is Graph Theory? What Is Graph theory. Discussion about Graph theory. Ecyclopedia or dictionary article about Graph theory. http://www.knowledgerush.com/kr/encyclopedia/Graph_theory/

6. Graph Theory: Facts, Discussion Forum, And Encyclopedia Article Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from http://www.absoluteastronomy.com/topics/Graph_theory

Home Discussion Topics Dictionary ... Login Graph theory Graph theory Topic Home Discussion Definition Overview In mathematics Mathematics Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.... and computer science Computer science Computer science or computing science is the study of the theoretical foundations of information and computation, and of practical techniques for their implementation and application in computer systems. It is frequently described as the systematic study of algorithmic processes that create,... graph theory is the study of graphs Graph (mathematics) 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... : mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of

7. Graph Theory - Wikinfo For an introduction to graph theory, see graph (mathematics). In mathematics and computer science, graph theory has for its subject matter the properties of graphs. http://www.wikinfo.org/index.php/Graph_theory

Graph theory From Wikinfo Jump to: navigation search For an introduction to graph theory, see graph (mathematics) In mathematics and computer science graph theory has for its subject matter the properties of graphs . Informally speaking, a graph is a set of objects called points or vertices connected by links called lines or edges . In a graph proper, which is by default undirected , a line from point A to point B is considered to be the same thing as a line from point B to point A . In a digraph , short for directed graph , the two directions are counted as being distinct arcs or directed edges Contents History Definition Drawing graphs Graph-theoretic data structures ... References History One of the first results in graph theory appeared in Leonhard Euler 's paper on Seven Bridges of Königsberg , published in . It is also regarded as one of the first topological results in geometry; that is, it does not depend on any measurements. This illustrates the deep connection between graph theory and topology In Gustav Kirchhoff published his Kirchhoff's circuit laws for calculating the voltage and current in electric circuits In Francis Guthrie posed the four color problem which asks if it is possible to color, using only four colors, any map of countries in such a way as to prevent two bordering countries from having the same color. This problem, which was only solved a century later in

8. The Math Forum - Math Library - Graph Theory The Math Forum's Internet Math Library is a comprehensive catalog of Web sites and Web pages relating to the study of mathematics. This page contains sites relating to Graph 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.

9. InterTran - Translate Between 1,482 Language Pairs Set on mathematics duck computer science, graph theory ice in spite of the fact that study shame graphs mathematical structures used dates back to forme pairwise comparative http://www6.tranexp.com:2000/Translate/index.shtml?from=nor&to=eng&type=

10. Graph Theory Summary And Analysis Summary | BookRags.com Graph theory summary with 21 pages of lesson plans, quotes, chapter summaries, analysis, encyclopedia entries, essays, research information, and more. http://www.bookrags.com/Graph_theory

11. Graph Theory - Wikibooks, Collection Of Open-content Textbooks This book was last edited on 25 June 2010, and is still under heavy construction. Content that is added is likely to be moved/deleted/edited significantly in a short amount of http://en.wikibooks.org/wiki/Graph_Theory

Graph Theory From Wikibooks, the open-content textbooks collection Jump to: navigation search This book is intended for advanced readers. Graph Theory is the study of nodes and the edges connecting those nodes, and topics such as combinatorics, networks, scheduling, and connectivity. Graph theory does not examine graphs as in Calculus (curves and other related concepts). Graph theory can be thought of as the "mathematician's connect-the-dots". What is Graph Theory? Graph Theory (graph theory) is the study of interactions between nodes (vertices) and edges (connections between the vertices). There are many applications of graph theory to mathematics, combinatorics, computer science and programming, engineering, networks and relationships, scheduling, and many more. What is a Graph? In contrast to the common knowledge of graph as a line or curve drawn on the cartesian(x,y) or or radial(r,theta) axes, in the context of graph thery, a Graph G=(V,E) consists of a set V of vertices and another set E of edges whose relation is defined by an unordered pair of vertices (v i ,v j ) related to an edge e k . The graphical representation of a graph can be done in various ways, the most common way being representation of vertices as dots and edges as lines connecting them. Graphs are used in diverse fields, computer networks being one of them.

12. 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. [

13. Graph Theory@Everything2.com A branch of mathematics involving the study of graph s, collections of point s (commonly called vertices or node s; this is the sense of node used on Everything) which are http://everything2.com/title/graph theory

14. Algorithmic Graph Theory Lecture notes and references by Rashid Bin Muhammad. 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

15. 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.

16. Graph Theory -- Graph Theory Textbooks And Resources The website www.graphtheory.com is sponsored by the mathematical textbooks of Professor Jonathan Gross of Columbia University. It provides comprehensive graph theory http://www.graphtheory.com/

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 The website www.graphtheory.com is sponsored by the mathematical textbooks of Professor Jonathan Gross of Columbia University. It provides comprehensive graph theory resources maintained by Daniel Sanders. New November 2007 click to enlarge cover Order through Amazon.com For Use With This New Text: Combinatorial Methods Toolkit Combinatorial Methods with Computer Applications List Price: Cat. #: ISBN: ISBN 10: Publication Date: Number of Pages: Availability: Not Yet Published PUBLISHER'S DESCRIPTION Provides a thorough, up-to-date treatment of combinatorics that covers topics such as asymptotics, graphs, and evaluating sums Presents the computer algorithms in easy-to-read pseudo-code Foreshadows difficult topics early in the book to prepare students for more in-depth discussions later on Incorporates definitions, theorems, proofs, examples, and nearly 300 illustrations as pedagogical elements of the exposition

17. Graph Theory Summary | BookRags.com Graph Theory. Graph Theory summary with encyclopedia entries, research information, and more. http://www.bookrags.com/eb/graph-theory-eb/

18. Graph Theory: Definition From Answers.com The mathematical study of the structure of graphs and networks. The body of techniques used in graphing functions in the plane. http://www.answers.com/topic/graph-theory

19. Graph Theory Jobs - Browse Keywords | Juju Job Search Browse graph theory jobs from 1,000s of job boards and employer web sites in one place. Juju makes your graph theory job search faster and more comprehensive. http://www.job-search-engine.com/keyword/graph-theory/

20. 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 How to contact me . 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

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