
	Where results make sense

Topic: Distance (graph theory)

	Graph theory - Wikipedia, the free encyclopedia
		Enumerative graph theory then rose from the results of Cayley and the fundamental results published by Pólya between 1935 and 1937 and the generalization of these by De Bruijn in 1959.
		The introduction of probabilistic methods in graph theory, specially in the study of Erdös and Rényi of the asymptotic probability of graph connexity is at the origin of yet another branch, known as random graph theory.
		Graph theory is also used to study molecules in chemistry and physics.
	en.wikipedia.org /wiki/Graph_theory (1884 words)

	Wikinfo \| Graph theory
		Graphs with weights can be used to represent many different concepts; for example if the graph represents a road network, the weights could represent the length of each road.The only information a weighted graph provides as such is (a) the vertices, (b) the edges and (c) the weights.
		Graph theory is the branch of mathematics that examines the properties of graphs.
		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.wikinfo.org /wiki.php?title=Graph_theory (2257 words)

	DIMACS Workshop on Geometric Graph Theory
		Graphs with a cyclic ordering on the vertices are known as `convex geometric graphs'; they model the combinatorial structure of systems of sides and diagonals in a convex polygon, and can thus be interpreted as geometric graphs whose vertex set is in convex position.
		A geometric graph is a graph drawn in the plane with straight line segments as edges connecting vertices that are assumed to be in general position.
		The fundamental question of extremal graph theory is to determine the maximum number ex(n, H) of edges in an H-free graph on n vertices, where H is a class of so-called forbidden subgraphs.
	dimacs.rutgers.edu /Workshops/GeometricGraph/abstracts.html (5604 words)

	[No title]
		Otherwise the graph is said to be disconnected The connected component of a graph G containing a given vertex v an element of V(G) is the largest sub-graph of G that contains v and is a connected graph.
		The girth of a graph is the length of the shortest circuit.
		A subtree of a graph G is a subgraph of G that is a tree.
	web.mit.edu /chungc/urop02/GraphTheory (2652 words)

	Boost Graph Library: Graph Theory Review
		Fundamentally, a graph consists of a set of vertices, and a set of edges, where an edge is something that connects two vertices in the graph.
		The primary property of a graph to consider when deciding which data structure to use is sparsity, the number of edges relative to the number of vertices in the graph.
		For the algorithm to keep track of where it is in the graph, and which vertex to visit next, BFS needs to color the vertices (see the section on Property Maps for more details about attaching properties to graphs).
	www.boost.org /libs/graph/doc/graph_theory_review.html (2374 words)

	Graphs Glossary
		A graph is bipartite if the vertices can be partitioned into two sets, X and Y, so that the only edges of the graph are between the vertices in X and the vertices in Y. Trees are examples of bipartite graphs.
		A chain in a graph is a sequence of vertices from one vertex to another using the edges.
		The closure of a graph G with n vertices, denoted by c(G), is the graph obtained from G by repeatedly adding edges between non-adjacent vertices whose degrees sum to at least n, until this can no longer be done.
	www-math.cudenver.edu /~wcherowi/courses/m4408/glossary.htm (1926 words)

	PlanetMath: Hamming distance
		This distance is applicable to encoded information, and is a particularly simple metric of comparison, often more useful than the city-block distance or Euclidean distance.
		The Hamming distance is a true metric, as it induces a metric space on the set of ordered lists of some fixed length.
		This is version 6 of Hamming distance, born on 2002-01-04, modified 2004-03-13.
	planetmath.org /encyclopedia/HammingDistance.html (138 words)

	Games on Graphs (Site not responding. Last check: 2007-10-08)
		The graphs of Graph Theory are not the same as the graphs which are used to plot or chart statistical information.
		The idea of "distance" in a graph is different from the "distance" we commonly measure with a tape measure, however, because we can stretch or shrink the edges of a graph to be any length at all.
		Similarly, the diameter of a graph is the distance between the two vertices of the graph that are farthest apart.
	www.cs.uidaho.edu /~casey931/mega-math/workbk/graph/grbkgd.html (1491 words)

	Graph theory glossary
		A coclique in a graph is a clique in its complementary graph (q.v.).
		girth (n.): The girth of a graph is the length of the shortest cycle(s) in the graph.
		When A,B are graphs, an isomorphism is a bijection from the vertices of A to the vertices of B such that any two vertices of A are adjacent if and only if their images in B are adjacent.
	www.math.harvard.edu /~elkies/FS23j.04/glossary_graph.html (1317 words)

	Intro to Graph Theory
		A graph is defined as a set of nodes and a set of lines that connect the nodes.
		A subgraph of a graph is a subset of its points together with all the lines connecting members of the subset.
		A local bridge of degree k is an edge whose removal causes the distance between the endpoints of the edge to be at least k.
	www.analytictech.com /mb021/graphtheory.htm (1984 words)

	Graph Theory Open Problems
		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.
		Paul O'Donnell has found a unit distance graph of girth 12 which cannot be 3-colored, but this graph has an incredibly large number of points.
		To get the square of an oriented graph (or any directed graph) you leave the vertex set the same, keep all the arcs, and for each pair of arcs of the form (u,v), (v,w), you add the arc (u,w) if that arc was not already present.
	dimacs.rutgers.edu /~hochberg/undopen/graphtheory/graphtheory.html (705 words)

	05C: Graph theory
		A graph is a set V of vertices and a set E of edges -- pairs of elements of V. This simple definition makes Graph Theory the appropriate language for discussing (binary) relations on sets, which is clearly a broad topic.
		A graph may be viewed as a one-dimensional CW-complex and hence studied with tools from Algebraic Topology, in particular, questions of planarity (and genus).
		Determining the genus of a graph is NP-complete.
	www.math.niu.edu /~rusin/known-math/index/05CXX.html (1204 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)

	Graph Theory
		So the emphasis for the final will be on using graph theory as a tool to formulate problems, asking only for you to be familiar with a reasonable proportion of the material we've covered in class, including at least one of the class presentations in addition to that of your own group.
		The distance between two vertices is the minimum length of all paths which connect them, where the length of a path is the number of edges in the path.
		The radius of a graph is the minimum eccentricity of the vertices, while the diameter of a graph is the maximum eccentricity of the vertices.
	www.georgetown.edu /faculty/kainen/graphtheory.html (3531 words)

	Graph Theory
		Graph Theory was born to study problems of this type.
		These pages are not intended to replace the standard texts in Graph Theory, rather to give a place on the web where some of the basic definitions can be found.
		In an undirected graph, this is obviously a metric.
	www.math.fau.edu /locke/GRAPHTHE.HTM (1165 words)

	The Math Forum - Math Library - Graph Theory
		A graph is a set V of vertices and a set E of edges - pairs of elements of V. This simple definition makes Graph Theory the appropriate language for discussing (binary) relations on sets.
		Among the topics of interest are topological properties such as connectivity and planarity (can the graph be drawn in the plane?); counting problems (how many graphs of a certain type?); coloring problems (recognizing bipartite graphs, the Four-Color Theorem); paths, cycles, and distances in graphs (can one cross the Königsberg bridges exactly once each?).
		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.
	mathforum.org /library/topics/graph_theory (2440 words)

	Graph Theory (math 224)
		A plane graph is a graph which is actually embedded in the plane so that each vertex corresponds to a point and each edge to a simple closed curve (or straight-line segment if you prefer) joining the points corresponding to its endpoints.
		The complement of a plane graph is a disjoint union of connected components which are called the _regions_ of the plane graph.
		Similarly, for graphs in the _torus_ (think "doughnut" or "inner tube") n-m+r = 0 and the corresponding upper bound on edges is m leq 3n; hence, average degree is at most 6 and so there must be a vertex of degree not exceeding 6 in any toroidal graph.
	www.georgetown.edu /faculty/kainen/graph-theory.html (3496 words)

	Graph Theory using the GRAPE package
		The girth of a graph is the length of a shortest cycle.
		On a graph that is simple we may check whether it can be expressed as the disjoint union of two sets, with edges only between the sets.
		The induced subgraph of a graph, given vertex list V is the graph containing only those vertices in V, and any edges between two elements of V that were in the original graph.
	www-groups.dcs.st-and.ac.uk /circa/gapstuff/gapfiles/grape.html (2601 words)

	Graph Theory
		Split students up into small groups, and have them explore other types of graphs with the graph applets.
		Explain that there are other types of graphs as well, and that some graphs can represent two types of graphs.
		Assign groups of students to one of the graphs on the sheet.
	www.shodor.org /succeed/mathcon/graphTheory.html (748 words)

	Distance (graph theory) - Wikipedia, the free encyclopedia
		In the mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path connecting them.
		The diameter of a graph is the maximum eccentricity of any vertex in the graph.
		A peripheral vertex in a graph of diameter d is one that is distance d from some other vertex—that is, a vertex that achieves the diameter.
	en.wikipedia.org /wiki/Distance_(graph_theory) (314 words)

	Math Forum - Problems Library - Middle School, Graph Theory
		In grades 6-8, the study of discrete mathematics may lead to explorations of graph theory.
		Other graph theory problems that might be adapted for use in the middle-school classroom can be found in the Discrete Math Problem of the Week.
		For relevant sites on the Web, browse and search Graph Theory in our Internet Mathematics Library; to find middle-school sites, go to the bottom of the page, set the searcher for middle school (6-8), and press the Search button.
	mathforum.org /library/problems/sets/middle_graphtheory.html (129 words)

	Amazon.com: Schaum's Outline of Graph Theory: Including Hundreds of Solved Problems: Books: V. K. Balakrishnan (Site not responding. Last check: 2007-10-08)
		I have bought and used many Schaum's outlines on various subjects in math and science, and I would say that this outline on graph theory is one of the worst.
		If you are already using a bad textbook for a class in graph theory, this book will only add to your collection of bad unreadable texts on the subject.
		In the second graph theory course that I took (to refresh and refine my understanding), the professor chose the Schaum text solely for its low cost--he thought he was doing the students a service.
	www.amazon.com /Schaums-Outline-Graph-Theory-Including/dp/0070054894 (1529 words)

	TCS - Studies - T-79.5203 Graph Theory
		Graph theory is arguably one of the most studied topics in contemporary discrete mathematics, and its theoretical and applied importance is constantly growing.
		The theory part covers basic types of graphs and central graph theoretic concepts such as distance, symmetry, coloring, connectivity, planarity, and so forth.
		The algorithm part reviews some of the central graph algorithms/problems such as depth- and breadth-first search together with their numerous applications, shortest path, minimum spanning tree, maximum matching, maximum flow, and so forth.
	www.tcs.hut.fi /Studies/T-79.5203 (420 words)

	Graph Theory: Industrial Drilling
		The distance between any two diamonds is less than 35.
		The distance between any diamond and any star is less than 35.
		The distance between any two of the green stars is less than 35, however.
	www.ibiblio.org /links/devmodules/graph_theory/compat/page37.html (210 words)

	Open Directory - Science: Math: Combinatorics: Graph Theory (Site not responding. Last check: 2007-10-08)
		A Constructive Approach to Graph Theory - Notes on a semiotic approach to constructing isomorphism invariants of graphs by John-Tagore Tevet.
		Getgrats: General Theory of Graph Transformation Systems - A research network funded by the European Commission.
		The Vertex Coloring Algorithm - A polynomial-time algorithm for coloring the vertices of a graph with a new constructive proof of Brooks' theorem by Ashay Dharwadker.
	dmoz.org /Science/Math/Combinatorics/Graph_Theory (549 words)

	[No title]
		Trees and Distance: properties of trees, distance in graphs, spanning trees, minimum spanning trees, shortest paths.
		Matchings and Factors: matchings in bipartite graphs, Hall's matching condition, min-max theorems.
		Planar Graphs: embeddings and Euler's formula, characterization of planar graphs (Kuratowski's theorem).
	www.math.neu.edu:16080 /grad/semconv/GraphTheory.doc (409 words)

Try your search on: Qwika (all wikis)