1. Graph Theory - Wikipedia, The Free Encyclopedia Image gallery graphs Concise, annotated list of graph theory resources for researchers. Retrieved from http//en.wikipedia.org/wiki/graph_theory 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 - Simple English Wikipedia, The Free Encyclopedia Retrieved from http//simple.wikipedia.org/wiki/graph_theory . Category 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.

3. 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:

4. 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 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.

5. 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.

6. Tree (graph Theory) - Wikipedia, The Free Encyclopedia Second Series 49 (3) 583�599, doi10.2307/1969046, http//jstor.org http://en.wikipedia.org/wiki/Tree_(graph_theory)

Tree (graph theory) From Wikipedia, the free encyclopedia Jump to: navigation search Trees A labeled tree with 6 vertices and 5 edges Vertices v Edges v Chromatic number v d e In mathematics , more specifically graph theory , a tree is an undirected graph in which any two vertices are connected by exactly one simple path . In other words, any connected graph without cycles is a tree. A forest is a disjoint union of trees. The various kinds of trees used as data structures in computer science are not really trees in this sense, but rather, types of ordered directed trees; see below. Contents Definitions Example Facts Enumeration ... edit Definitions A tree is an undirected simple graph G that satisfies any of the following equivalent conditions: G is connected and has no cycles G has no cycles, and a simple cycle is formed if any edge is added to G G is connected, and it is not connected anymore if any edge is removed from G G is connected and the 3-vertex complete graph K is not a minor of G Any two vertices in G can be connected by a unique simple path If G has finitely many vertices, say

7. Category:Graph Theory - Wikipedia, The Free Encyclopedia Retrieved from http//en.wikipedia.org/wiki/Categorygraph_theory http://en.wikipedia.org/wiki/Category:Graph_theory

Category:Graph theory From Wikipedia, the free encyclopedia Jump to: navigation search The main article for this category is Graph theory Wikimedia Commons has media related to: Graph theory Graph theory is the branch of mathematics that examines the properties of mathematical graphs . See glossary of graph theory for common terms and their definition. Informally, this type of graph is a set of objects called vertices (or nodes) connected by links called edges (or arcs), which can also have associated directions. Typically, a graph is depicted as a set of dots (i.e., vertices) connected by lines (i.e., edges), with an arrowhead on a line representing a directed arc. Such graphs can be used to represent and analyze a variety of systems and problems, including colorability problems, shortest path algorithms and spanning trees. For info on other types of graphs see graphs Resources: Wikipedia:Graphic Lab/Image workshop meta:Philip Greenspun illustration project . Creation and improvement of illustrations for Wikimedia. Commons:Chart and graph resources Subcategories This category has the following 23 subcategories, out of 23 total.

8. Field:Graph Theory - Math Images And so on. Retrieved from http//mathforum.org/mathimages/index.php/Field http://mathforum.org/mathimages/index.php/Field:Graph_Theory

Field:Graph Theory From Math Images Jump to: navigation search Add to NSDL View in NSDL ... Edit Metadata Basic Description of Graph Theory Example of a planar graph (top) and a non-planar graph (bottom) Graph theory is the study of graphs . A graph is informally a collection of points, known as vertices, connected by lines, known as edges. Basic Terminology Acyclic graph- a graph which contains no cycles Adjacent - two vertices are said to be adjacent if an edge connects them. Cycle- A path for which the first element is the same as the final element Directed graph (or digraph)- a graph for which all edges are assigned a direction. That is, for an edge between an arbitrary vertex A and vertex B, assigning a direction means the edge is either directed towards vertex A or towards vertex B. Eulerian Circuit- A cycle which contains all of the edges of a graph. This idea was inspired by the the Seven Bridges of Königsberg problem. Hamiltonian Cycle- A cycle which contains all of a graph's vertices. Hamiltonian Path - A path which contains all of a graph's vertices. Path - A sequence of distinct graph edges Planar Graph - A graph that can be drawn such that no two edges overlap each other.

9. Graph Theory : Good Math, Bad Math Search. Profile. markcc.jpg. Mark ChuCarroll (aka MarkCC) is a PhD Computer Scientist, who works for Google as a Software Engineer. http://scienceblogs.com/goodmath/goodmath/graph_theory/

10. CiteULike: JeffreyDemaine's Graph_theory [6 Articles] Recent papers added to JeffreyDemaine s library classified by the tag graph_theory. You can also see everyone s graph_theory. http://www.citeulike.org/user/JeffreyDemaine/tag/graph_theory

11. 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/

12. CiteULike: Sobolevnrm's Graph_theory [26 Articles] posted to graph_theory software signature management by sobolevnrm on 2010 http://www.citeulike.org/user/sobolevnrm/tag/graph_theory

13. CiteULike: Karthikraman's Graph_theory [2 Articles] Recent papers added to karthikraman s library classified by the tag http://www.citeulike.org/user/karthikraman/tag/graph_theory

14. Graph Theory - Definition graph_theory. Graph theory Definition. In mathematics and computer science, graph theory studies the properties of graphs. Informally, a graph is a set of http://www.wordiq.com/definition/Graph_theory

Graph theory - Definition In mathematics and computer science graph theory studies the properties of graphs . Informally, a graph is a set of objects called vertices (or Nodes) connected by links called edges (or Arcs) which can be directed. Typically, a graph is designed as a set of dots (the vertices) connected by lines (the edges). A graph with 6 vertices and 7 edges. Structures that can be represented as graphs are ubiquitous, and many problems of practical interest can be represented by graphs. The link structure of Wikipedia could be represented by a directed graph: the vertices are the articles in Wikipedia and there's a directed edge from article A to article B if and only if A contains a link to B . The development of algorithms to handle graphs is therefore of major interest in computer science A graph structure can be extended by assigning a weight to each edge, or by making the edges to the graph directional ( A links to B , but B does not necessarily link to A , as in webpages), technically called a digraph . Within graph theory, a digraph with weighted edges is called a network.

15. Node (graph Theory) - Definition Node_(graph_theory). Node (graph theory) Definition. This article just http://www.wordiq.com/definition/Node_(graph_theory)

Node (graph theory) - Definition This article just presents the basic definitions. For a broader view see graph theory For another mathematical use of "graph", see graph of a function A graph with 6 vertices and 7 edges. In mathematics and computer science a graph is the basic object of study in graph theory . Informally, a graph is a set of objects called vertices connected by links called edges . Typically, a graph is depicted as a set of dots (the vertices) connected by lines (the edges). Depending on the application some edges can directed. Contents showTocToggle("show","hide") 1 Definitions 1.1 Undirected graph 1.2 Directed graph 1.3 Mixed graph ... 4 Generalizations Definitions Definitions in graph theory vary in the literature. Here are the conventions used in this encyclopedia. Undirected graph An undirected graph or graph G is an ordered pair G V E ) with V a set of vertices or nodes E a set of unordered pairs of distinct vertices, called edges or lines Directed graph A directed graph digraph or quiver G is an ordered pair G V A ) with V a set of vertices or nodes A a set of ordered pairs of vertices called directed edges arcs or arrows Note that a directed graph is allowed to have loops , that is, edges where the start and end vertices are the same.

16. Videolectures Category: Graph Theory Topic Top � Mathematics � Graph Theory. View order. Hot Popular Just published. Recent Top Voted. Topic taxonomy. No subtopics. Feeling lucky http://videolectures.net/Top/Mathematics/Graph_Theory/

Log in Register New User Register ... Blog Topic: Top Mathematics View order Hot Popular Just published Recent Top Voted Topic taxonomy No subtopics Feeling lucky Type of content Event Lecture Tutorial Keynote Interview External Other... Language English Slovenian French German Dutch Croatian Other... Year From: (any) To: (any) ...Search a Keyword $('#tm_browse').addClass('current'); Please wait... EDITOR’S PICKS What showbiz has to do with it - Hans Rosling Lecture 1 - Introductions: Why Does the Civil War Era Have a Hold on American Historical Imagination? - David W. Blight European Investment Fund - role in the Tech Transfer market - Yannis Tsakiris Time Series Gene Expression Data Classification via L1-norm Temporal SVM - Carlotta Orsenigo FEATURED CONFERENCES Environmental Information Systems and Services: Infrastructures and Platforms Workshop 2010 Yale HIST 119 - The Civil War and Reconstruction Era, 1845-1877 with Professor David Blight - David W. Blight 3rd International Technology Transfer Conference MIT World Series: Solutions that Scale to Meet the Energy Challenge: Technology, Policy and Entrepreneurship BLOG POSTS Top 40 Sources for Open Courseware videos We are looking for new bloggers Review: "Ugliness is infinite, like God"

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18. 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

19. Connectivity_(graph_theory) Encyclopedia Topics | Reference.com Encyclopedia article of Connectivity_(graph_theory) at Reference.com compiled from comprehensive and current sources. http://www.reference.com/browse/Connectivity_(graph_theory)

20. Distance_(graph_theory) | Define Distance_(graph_theory) At Dictionary.com Distance_(graph_theory). no dictionary results. Graphing Pre-Calculus http://dictionary.reference.com/browse/Distance_(graph_theory)

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