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Topic: Connectivity (graph theory)

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Glossary of graph theory

graph of a function

graph mathematics

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directed graphs

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	Connectivity (graph theory) - Wikipedia, the free encyclopedia
		The connectivity of a graph is an important measure of its robustness as a network.
		One of the most important facts about connectivity in graphs is Menger's theorem, which characterizes the connectivity and edge-connectivity of a graph in terms of the number of independent paths between vertices.
		In computational complexity theory, SL is the class of problems log-space reducible to the problem of determining whether two vertices in a graph are connected, which was proved to be equal to L by Omer Reingold in 2004.
	en.wikipedia.org /wiki/Connectivity_(graph_theory) (812 words)

	GIS/EM4 - Landscape Connectivity: A Conservation Application of Graph Theory
		Graph theory is a widely applied framework in information technology, and is primarily concerned with maximally efficient flow or connectivity in networks.
		Graphs are defined by two data structures: one that describes the nodes and one that describes the edges.
		The landscape is fundamentally connected for mink and unconnected for prothonotary warblers.
	www.colorado.edu /research/cires/banff/pubpapers/195 (1214 words)

	PlanetMath: ${k}$-connected graph
		Connectivity of graphs, when it isn't specified which flavor is intended, usually refers to vertex connectivity, unless it is clear from the context that it refers to edge connectivity.
		Note that “removing a vertex” in graph theory also involves removing all the edges incident to that vertex.
		For directed graphs there are two notions of connectivity (“weak” if the underlying graph is connected, “strong” if you can get from everywhere to everywhere).
	planetmath.org /encyclopedia/KConnectedGraph.html (287 words)

	Glossary of graph theory - Wikipedia, the free encyclopedia
		Graph theory is a growth area in mathematical research, and has a large specialized vocabulary.
		Likewise, a graph G is said to be homomorphic to a graph H if there is a mapping, called a homomorphism, from V(G) to V(H) such that if two vertices are adjacent in G then their corresponding vertices are adjacent in H.
		Connectivity extends the concept of adjacency and is essentially a form (and measure) of concatenated adjacency.
	en.wikipedia.org /wiki/Glossary_of_graph_theory (5920 words)

	Intro to Graph Theory (Site not responding. Last check: 2007-10-14)
		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 bridge is an edge whose removal from a graph increases the number of components (disconnects the graph).
	www.analytictech.com /networks/graphtheory.htm (1221 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.
		Bound δ (of a graph embedded in on a surface)
	www.math.fau.edu /locke/GRAPHTHE.HTM (1165 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)

	Connected (Site not responding. Last check: 2007-10-14)
		Connected category, a category in which, for every two objects, there is at least one morphism connecting them
		Connected space, a topological space which cannot be written as the disjoint union of two or more nonempty spaces
		Connection (mathematics), a way of specifying a derivative of a vector field along another vector field on a manifold
	www.brainyencyclopedia.com /encyclopedia/c/co/connected.html (244 words)

	``Introduction to Graph Theory'' (2nd edition)
		"Even graph" is my compromise expression for the condition that all vertex degrees are even, and I will continue to use "cycle" for a 2-regular connected graph, "circuit" for a cyclically-edge-ordered connected even graph, and "circuit" for a minimal dependent set in a matroid.
		Most research and applications in graph theory concern graphs without multiple edges or loops, and often multiple edges can be modeled by edge weights.
		Letting "graph" forbid loops and multiple edges simplifies the first notion for students, making it possible to correctly view the edge set as a set of vertex pairs and avoid the technicalities of an incidence relation in the first definition.
	www.math.uiuc.edu /~west/igt/index.html (1095 words)

	Graph Theory
		The text is "Introduction to Graph Theory" by Richard J. Trudeau, which is in paperback from Dover Publications, NY, 1994; still in print and available in the bookstore or from amazon.com - here is a picture.
		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 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 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)

	Diskret matematik (Site not responding. Last check: 2007-10-14)
		Graph theory is the mathematical abstraction of networks such as transportation networks, road-and railway networks, communication networks, molecules, and social networks.
		Early inspirations for graph theory were the mathematical foundation of electrical networks and coloring problems, in particular the Four Color Problem.
		The research at MAT is primarily centered around chromatic graph theory, graph connectivity, extremal problems, and topological aspests.
	www.mat.dtu.dk /Forskning/DiskretMat.aspx (246 words)

	TCS - Studies - S-72.343 / T-79.165 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.
		Here one central aim is to understand the connection between a mathematical result and the algorithm that exploits it.
	www.tcs.hut.fi /Studies/T-79.165 (461 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)

	An overview on Graph Theory (Site not responding. Last check: 2007-10-14)
		A graph is a very simple structure consisting of a set of vertices and a family of lines (possibly oriented), called edges (undirected) or arcs (directed), each of them linking some pair of vertices.
		The number of concepts that can be defined on graphs is very large, and many generate deep problems or famous conjectures (for instance the four colour problem).
		We present in an annex a small bibliographical reference on Graph Theory, and a more precise description of our research topics.
	www-leibniz.imag.fr /GRAPH/english/overview.html (332 words)

	Amazon.com: Schaum's Outline of Graph Theory: Including Hundreds of Solved Problems: Books: V. K. Balakrishnan (Site not responding. Last check: 2007-10-14)
		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 (1495 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)

	Random Lifts of Graphs I: General Theory and Graph Connectivity (ResearchIndex)
		245 Graphs and Hypergraphs (context) - Berge - 1975
		11 Topology of nite graphs (context) - Stallings - 1983
		2 Every connected regular graph of even degree is a schreier c..
	citeseer.ist.psu.edu /441224.html (321 words)

	Amazon.com: Graph Theory: Books: Frank Harary (Site not responding. Last check: 2007-10-14)
		An effort has been made to present the various topics in the theory of graphs in a logical order, to indicate the historical background, and to clarify the exposition by including figures to illustrate concepts and results.
		It is no coincidence that graph theory has been independently discovered many times, since it may quite properly be regarded as an area of applied mathematics Read the first page
		If you are looking for examples of computer algorithms, look elsewhere; the closest this will get you is to "existence proofs", which is showing that something (such as a hamiltonian cycle) exists in a graph that has thus-and-such number of points or edges, but not tell you which sequence of points/edges make up that something.
	www.amazon.com /Graph-Theory-Frank-Harary/dp/0201410338 (1137 words)

	Syllabus for CSC/Math 4408, Dr. Ellen Gethner (Site not responding. Last check: 2007-10-14)
		Connecteness: component, maximal, number of connected components,induced subgraph, distance between two vertices, the Peterson Graph.
		Next, construct such a graph to show that the edge bound is sharp.
		Characterization of Planar Graphs: Subdivision of a graph.
	carbon.cudenver.edu /~egethner/GraphTheory/GraphTheory06.html (1194 words)

	The Graph Theorists' Home Page Guide
		First of all, if you're a graph theorist or some person with strong interest in graph theory (you need not to be a mathematician!), and if you have a homepage but don't find a link to it on this page, please contact me as described above.
		PIGALE is a graph editor with an interface to the LEDA library and with many algorithms implemented essentially concerning planar graphs.
		"Graph Theory and Its Applications" (together with Jay Yellen), "a comprehensive applications-driven textbook that provides material for several different courses in graph theory." This site also provides links to other graph theoretical and mathematical resources.
	www.joergzuther.de /math/graph/homes.html (8736 words)

	mathgradcoursecatalog.html
		Theory of ordinary and functional differential equations: basic existence theorems, linear systems, stability theory, periodic and almost-periodic solutions.
		Topics include matching theory, connectivity, graph coloring, planarity, extremal graph theory, and the main techniques (elementary, probabilistic, algebraic, and polyhedral) for analyzing the structure and properties of graphs.
		Problems in the qualitative theory of nonlinear ordinary and functional differential equations that arise in such subjects as the Hudgkin-Huxley theory, hormonal control systems, and rhythms in physiology.
	www.math.rutgers.edu /grad/courses/mathgradcoursecatalog.html (1375 words)

	Algorithmic Graph Theory - Cambridge University Press (Site not responding. Last check: 2007-10-14)
		This is a textbook on graph theory, especially suitable for computer scientists but also suitable for mathematicians with an interest in computational complexity.
		Although it introduces most of the classical concepts of pure and applied graph theory (spanning trees, connectivity, genus, colourability, flows in networks, matchings and traversals) and covers many of the major classical theorems, the emphasis is on algorithms and thier complexity: which graph problems have known efficient solutions and which are intractable.
		A number of exercises and outlines of solutions are included to extend and motivate the material of the text.
	www.cambridge.org /catalogue/catalogue.asp?isbn=0521288819 (247 words)

	Graph Theory WS 03-04
		This course is an introduction to the theory of graphs intended for students in mathematics and computer science/engineering students with an interest in theory.
		Possible topics include: degrees, paths, trees, cycles, Eulerian circuits, bipartite graphs, extremality, matchings, connectivity, network flows, vertex and edge colorings, Hamiltonian cycles and planarity.
		In lecture we will follow the textbook "Introduction to Graph Theory" by Doug West.
	www.ti.inf.ethz.ch /ew/courses/GT03 (371 words)

	Connectedness (Site not responding. Last check: 2007-10-14)
		We might wish to call a topological space connected if each pair of points in it is joined by a path.
		For example, in graph theory, a connected graph is one from which we must remove at least one vertex to create a disconnected graph.
		Similarly, a graph is 2-connected if we must remove at least two vertices from it, to create a disconnected graph.
	www.experiencefestival.com /connectedness (666 words)

	Intro Graph Theory: Components Connectivity (Site not responding. Last check: 2007-10-14)
		Two vertices of a graph that are joined by a path are said to belong to the same component of the graph.
		If the whole graph is one component, then it is said to be connected.
		Thus the components are connected subgraphs which are not contained in larger connected subgraphs.
	www.physicsforums.com /showthread.php?t=10258 (281 words)

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