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# Topic: Graph (mathematics)

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 Encyclopedia :: encyclopedia : Graph (mathematics) (via CobWeb/3.1 planetlab2.cs.umd.edu)   (Site not responding. Last check: 2007-10-08) A quiver is sometimes said to be simply a directed graph, but in practice it is a directed graph with vector spaces attached to the vertices and linear transformations attached to the arcs. In a weighted graph or digraph, each edge is associated with some value, variously called its cost, weight, length or other term depending on the application; such graphs arise in many contexts, for example in optimal route problems such as the traveling salesman problem. Every graph gives rise to a matroid, but in general the graph cannot be recovered from its matroid, so matroids are not truly generalizations of graphs. www.hallencyclopedia.com.cob-web.org:8888 /topic/Graph_(mathematics).html   (1382 words)

 AllRefer.com - graph (Mathematics) - Encyclopedia The graph of a function y=f (x) is the set of points with coordinates [x, f (x)] in the xy-plane, when x and y are numbers. Statistics makes extensive use of both line graphs and bar graphs, in which the lengths of the various bars show the quantities to be compared. Graph is also a mathematical term used in combinatorics to designate a geometric object consisting of vertices and edges (joining pairs of vertices). reference.allrefer.com /encyclopedia/G/graph.html   (215 words)

 Graph theory   (Site not responding. Last check: 2007-10-08) Graph theory is the branch of mathematics that examines the properties of graphs. Informally a graph is a set of called vertices (or nodes) connected by links called edges (or arcs). In general there are four ways to a graph in a computer system: The list representation the incidence matrix representation adjacency list representation and the adjacency matrix representation. www.freeglossary.com /Graph_theory   (1059 words)

 Graph -- from Wolfram MathWorld In elementary mathematics, "graph" refers to a function graph or "graph of a function," i.e., a plot. The edges, vertices, or both of a graph may be assigned specific values, labels, or colors, in which case the graph is called a labeled graph. A directed graph in which each edge is given a unique direction (i.e., edges may not be bidirected and point on both directions as once) is called an oriented graph. mathworld.wolfram.com /Graph.html   (656 words)

 Graph Theory - Mathematics and the Liberal Arts The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Ascher discusses geometric characteristics of the graphs (for example, many are regular of degree 4), and algorithms for drawing the curves. Other types of mathematical ideas from Malekula include a drum signaling system with rhythms for each clan, rank, grade of pig, and special phrases, and a six-class marriage system which the elders explained with diagrams in the sand. math.truman.edu /~thammond/history/Graphs.html   (1358 words)

 Ideas, Concepts, and Definitions   (Site not responding. Last check: 2007-10-08) 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. 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. www.c3.lanl.gov /mega-math/gloss/graph/gr.html   (215 words)

 Using Data and Statistics A line graph is a way to summarize how two pieces of information are related and how they vary depending on one another. Bar graphs consist of an axis and a series of labeled horizontal or vertical bars that show different values for each bar. A double bar graph is similar to a regular bar graph, but gives 2 pieces of information for each item on the vertical axis, rather than just 1. www.mathleague.com /help/data/data.htm   (1241 words)

 Games on Graphs   (Site not responding. Last check: 2007-10-08) 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. Graph theory has been instrumental for analyzing and solving problems in areas as diverse as computer network design, urban planning, and molecular biology. www.c3.lanl.gov /mega-math/workbk/graph/graph.html   (88 words)

 Graph - Wikipedia, the free encyclopedia Graph (mathematics), a structure of vertices and edges in graph theory Graph (data structure), a data structure representing a graph HMS Graph (P715), a submarine of the Royal Navy. en.wikipedia.org /wiki/Graph   (149 words)

 Graph Theory In an undirected graph, this is obviously a metric. A non-null graph is connected if, for every pair of vertices, there is a walk whose ends are the given vertices. A connected graph is therefore a graph with exactly one connected component. www.math.fau.edu /locke/graphthe.htm   (1165 words)

 Amazon.ca: Discrete Mathematics with Graph Theory: Books: Edgar G. Goodaire,Michael M. Parmenter   (Site not responding. Last check: 2007-10-08) Discrete mathematics is quite different from other areas in mathematics which you may have already studied, such as algebra, geometry, or calculus. As a textbook used for discrete mathematics and graph theory, there are many topics which must be covered. Graph theory is the subject of Chapters 9 through 15, and again we find that there is more material here than can be successfully treated in thirty-three lectures. www.amazon.ca /Discrete-Mathematics-Graph-Theory-Goodaire/dp/0131679953   (2969 words)

 Discrete Mathematics and Graph Theory Discrete mathematics is the study of finite systems and includes such areas as combinatorics, graph theory, algorithms and optimization. On the international level, research activity in discrete mathematics has increased very strongly over the last 20 years, in part stimulated by close relations with the expanding area of theoretical computer science. Among the specific topics being studied are graph colouring theory, extremal graph theory, directed graphs, network flows, scheduling problems, algorithms and complexity theory. www.imada.sdu.dk /Research/discrete_math.php   (181 words)

 Graph (mathematics) - Wikipedia, the free encyclopedia A distinction between a directed graph and an oriented simple graph is that if x and y are vertices, a directed graph allows both (x,y) and (y,x) as edges, while only one is permitted in an oriented graph. In a complete bipartite graph, the vertex set is the union of two disjoint subsets, W and X, so that every vertex in W is adjacent to every vertex in X but there are no edges within W or X. In a bipartite graph, the vertices can be divided into two sets, W and X, so that every edge has one vertex in each of the two sets. en.wikipedia.org /wiki/Graph_(mathematics)   (1764 words)

 graph theory -- graph theory textbooks and resources The superior explanations, broad coverage, and abundance of illustrations and exercises that positioned this as the premier graph theory text remain, but are now augmented by a broad range of improvements. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology. Authors explore the role of voltage graphs in the derivation of genus formulas, explain the Ringel-Youngs theorem—a proof that revolutionized the field of graph theory—and examine the genus of a group, including imbeddings of Cayley graphs. www.graphtheory.com   (991 words)

 Wiley::Graph Theory This mathematically rigorous introduction is tempered and enlivened by numerous illustrations, revealing examples, seductive applications, and historical references. These strands center, respectively, around matching theory; planar graphs and hamiltonian cycles; topics involving chordal graphs and oriented graphs that naturally emerge from recent developments in the theory of graphic sequences; and an edge coloring strand that embraces both Ramsey theory and a self-contained introduction to Pólya's enumeration of nonisomorphic graphs. In the edge coloring strand, the reader is presumed to be familiar with the disjoint cycle factorization of a permutation. www.wiley.com /WileyCDA/WileyTitle/productCd-0471389250.html   (375 words)

 Games on Graphs Each story can be acted out on a graph that is drawn on the floor, with a student taking the part of each one of the characters. Students can also play the games on a table using a graph that is drawn on a piece of paper for a game board and moving marking pieces that show the actions of the characters. Because the distances in these graphs are different from the graph in The Land of Many Ponds, the students need more complex strategies to play that they had to use with that particular graph. www.c3.lanl.gov /mega-math/workbk/graph/grgsm.html   (1107 words)

 Graph Theory Tutorials   (Site not responding. Last check: 2007-10-08) This is the home page for a series of short interactive tutorials introducing the basic concepts of graph theory. 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. 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. www.utm.edu /departments/math/graph   (282 words)

 Charts and Graphs   (Site not responding. Last check: 2007-10-08) On line and bar graphs, the x and y axes must be appropriately labeled with correct unit of measure (in metrics where applicable). This kind of graph is needed to show the effect of an independent variable on a dependent variable. A circle graph is used to show how a part of something relates to the whole. www.twingroves.district96.k12.il.us /ScienceInternet/ChartsGraphs.html   (437 words)

 Graph Paper! This graph paper is a must for any student doing extensive graphing. This graph paper is best when you have a lot of graphs to make. Plain Large Grid Graph Paper with increased margins. www.mathematicshelpcentral.com /graph_paper.htm   (511 words)

 Amazon.fr : Algebraic Graph Theory: Livres en anglais: Norman L. Biggs   (Site not responding. Last check: 2007-10-08) In this substantial revision of a much-quoted monograph first published in 1974, Dr. Biggs aims to express properties of graphs in algebraic terms, then to deduce theorems about them. In the first section, he tackles the applications of linear algebra and matrix theory to the study of graphs; algebraic constructions such as adjacency matrix and the incidence matrix and their applications are discussed in depth. There follows an extensive account of the theory of chromatic polynomials, a subject that has strong links with the "interaction models" studied in theoretical physics, and the theory of knots. www.amazon.fr /Algebraic-Graph-Theory-Norman-Biggs/dp/0521458978   (342 words)

 Line Graphs   (Site not responding. Last check: 2007-10-08) So, for example, if you wanted to graph the height of a ball after you have thrown it, you could put time along the horizontal, or x-axis, and height along the vertical, or y-axis. This is done by either not using consistent scales on the axes, meaning that the value in between each point along the axis may not be the same, or when comparing two graphs using different scales for each. Based on your observations of the graph, make a prediction about what the wage might be in the year 2000. www.mste.uiuc.edu /courses/ci330ms/youtsey/lineinfo.html   (339 words)

 Graph Theory -- from Wolfram MathWorld The mathematical study of the properties of the formal mathematical structures called graphs. Graph Connections: Relationships Between Graph Theory and Other Areas of Mathematics. Tutte, W. Graph Theory as I Have Known It. mathworld.wolfram.com /GraphTheory.html   (303 words)

 Amazon.com: Introduction to Graph Theory (Dover Books on Advanced Mathematics): Books: Richard J. Trudeau   (Site not responding. Last check: 2007-10-08) Requiring only high school algebra as mathematical background, the book leads the reader from simple graphs through planar graphs, Euler’s formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, and a discussion of The Seven Bridges of Konigsberg. To give an idea of the depth of this book, I read this book in about 6 hours prior to taking a course in graph theory (an undergraduate and graduate student mixed course), and the material in the book was covered in class in about 4 lectures (there were about 30 lectures in the course). Trudeau has done a fabulous job of introducing graph theory in a way which is understandable and intellectually provocative. www.amazon.com /Introduction-Graph-Theory-Advanced-Mathematics/dp/0486678709   (1190 words)

 Mathematics Help Central Home Mathematics is a challenging subject that mystifies many. There's plenty of lecture notes, helpful links, personally developed graph paper, and a little section about why I love math. I strive to provide accurate and error-free documentation concerning all aspects of mathematics. www.mathematicshelpcentral.com   (124 words)

 Open Questions: Combinatorics, Graph Theory, and Computation The problems of traversing a graph so that each edge is crossed exactly once is compared with graph traversal where each vertex is encountered exactly once. See also Graph (mathematics), Glossary of graph theory. As usually described, the complexity of a computation is evaluated in terms of some specific computational model -- some sort of abstract computing device. www.openquestions.com /oq-ma004.htm   (550 words)

 The Standards Site: Handy graph Handy graph is a simple program that draws block graphs. Pupils can enter their own graph title and label the axes. As they enter their data they see the block graph created. www.standards.dfes.gov.uk /primary/publications/mathematics/12880   (152 words)

 Grammatica -- from Mathematica Information Center   (Site not responding. Last check: 2007-10-08) Grammatica is a library of Mathematica functions for algebraic graph transformation, built on top of the Combinatorica package written by Steven Skiena. The implementation takes the form of a package, and it consists of Mathematica functions for representing, manipulating, displaying and transforming graphs, as well as functions implementing some algebraic operations on graphs. It supports both interactive and automatic application of double-pushout graph productions, being therefore both a teaching aid and a research tool for algebraic graph transformation. library.wolfram.com /infocenter/MathSource/5486   (131 words)

 Amazon.com: Discrete Mathematics with Graph Theory (2nd Edition): Books: Edgar G. Goodaire,Michael M. Parmenter,Edgar G ...   (Site not responding. Last check: 2007-10-08) However, I will not be adopting it because of the large amount of graph theory, which is approximately forty percent of the book. Therefore, while the book is not suitable for my needs, it would be a perfect fit for anyone teaching discrete mathematics where there was an emphasis on graph theory. Although discrete mathematics is not meant to be all that numerically focused, I do not recommend using this text at all. www.amazon.com /Discrete-Mathematics-Graph-Theory-2nd/dp/0130920002   (1635 words)

 gmane.comp.mathematics.graph I just ran across this message in a discussion about graphing for students: I just encourage students to download and install the Word and PowerPoint add-in called Graph (www.padowan.dk). To draw a graph, go into the INSERT menu, select OBJECT, then find "Graph" or "Graph system." This is the first time I have heard of this feature - I tried it and it really works! What would be awesome is if you could have the option the scale the legend box, becasue when I paste my graph into a document, I usually scale the whole thing down a bit, but then the legend becomes uninteligiable. blog.gmane.org /gmane.comp.mathematics.graph   (982 words)

 Mathematics I am a Professor at the Department of Mathematics of Politecnico di Milano. Graph theory is dealt with at all levels, form basics to current research subjects. This is a research center for Discrete Mathematics and Computer Science at Rutgers University. www.angelfire.com /mi/raffaele55/math.html   (248 words)

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