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Topic: Cut vertex

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vertex figures

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	Graph Theory Lecture Notes 2a
		The neighborhood of a vertex v, denoted N(v), is the subgraph induced by v and all of its neighbors.
		Adding a vertex or an edge is as simple as it sounds, but note that adding a vertex is not, in general, the opposite of removing a vertex...
		If a new vertex v is joined to each of the pre-existing vertices of a graph G, then the resulting graph is called the join of G and v (or the suspension of G from v), and is denoted by G + v.
	www-math.cudenver.edu /~wcherowi/courses/m4408/gtaln2.html (809 words)

	Vertex Shading
		When a vertex is broken, there is one vertex for each face.
		We can paint each vertex on the harp manually using VertexPaint, but there is a better and more efficient way to create a first cut vertex shading.
		Drums are vertex shaded, so that I could use a very small wooden texture to render the side of the drum, while dedicating 2/3 of the texture budget for the drum face (texture and cutout).
	www.fred-hsu.com /there/developer/vertex_shading (3301 words)

	Definitions
		Degree: The degree (or valence) of a vertex is the number of edges connected to that vertex.
		Peripheral node: a vertex v in G is a peripheral node iff its eccentricity equals the diameter of G. Density: Basically, a graph is dense if it contains many edges and sparse if it contains only few edges.
		Cut vertex: In a connected graph, a cut vertex is a vertex that if removed, causes the graph not to be connected anymore.
	www.cs.utk.edu /~doucet/graph/definitions.html (538 words)

	Glossary of graph theory - Wikipedia, the free encyclopedia
		A vertex of degree 0 is an isolated vertex.
		A vertex of degree 1 is a leaf.
		A cut vertex, or articulation point, is a vertex whose removal disconnects the remaining subgraph.
	en.wikipedia.org /wiki/Glossary_of_graph_theory (5956 words)

	600-cell cross-section sequence
		Each vertex is shared by the 20 tetrahedra which are clustered around it.
		As we cut closer to the center of the 600-cell, we are cutting deeper and deeper into the 600-cell, so the icosahedrons get bigger.
		We've cut from vertex to opposite face (red, and dark orange cells), or from edge to opposite edge (orange cells), or along an edge (golden cells).
	www.cs.utah.edu /~gk/peek/600slice/index.html (605 words)

	Cut vertex - Wikipedia, the free encyclopedia (via CobWeb/3.1 planetlab2.tamu.edu) (Site not responding. Last check: 2007-10-29)
		In mathematics and computer science, a cut vertex or articulation point is a vertex of a graph such that removal of the vertex causes an increase in the number of connected components.
		A bridge is an edge analogous to a cut vertex; that is, the removal of a bridge increases the number of connected components of the graph.
		In a tree, every vertex with degree greater than 1 is a cut vertex.
	en.wikipedia.org.cob-web.org:8888 /wiki/Cut_vertex (256 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-29)
		Each vertex of the pyramid will be "R" distance from the center of the icosahedron.
		When you cut the vertex off, each equilateral triangle turns into a hexagon, and the cut off bit is a five-sided pyramid.
		The distance from each vertex of the base to the center of the base is 1 unit.
	mathforum.org /library/drmath/view/63013.html (1274 words)

	Conic Sections (Site not responding. Last check: 2007-10-29)
		When the cutting plane is perpendicular to the axis of symmetry, the elliptic section reduces to its particular case, a circle.
		A plane through the vertex that meet a cone in other points may be either tangent to the cone at one of the generating lines or cross the cone at two straight lines that meet at the vertex.
		Seeing the former case as the limiting configuration of the latter, it's customary to say that in both cases the section consists of two straight lines, that coincide when the plane is tangent to the cone.
	www.cut-the-knot.org /proofs/conics.shtml (594 words)

	The CTK Exchange Forums
		ABC is labeled counterclockwise, the y-coordinate of the vertex B is positive.
		ABC is labeled clockwise, the y-coordinate of the vertex B is negative.
		The line cutting the triangle area in half intersect the triangle in 2 points: P (on the triangle side a = CB) and S (on the triangle side b = CA).
	www.cut-the-knot.org /htdocs/dcforum/DCForumID3/248.shtml (3870 words)

	vertex - definition of vertex by the Free Online Dictionary, Thesaurus and Encyclopedia. (via CobWeb/3.1 ... (Site not responding. Last check: 2007-10-29)
		What we call the vertex of the Brain is really its base: and what we call its base is really its vertex: it is simply a question of nomenclature.
		Our courses were converging like the sides of an angle, the vertex of which was at the edge of the fog-bank.
		This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional.
	www.thefreedictionary.com.cob-web.org:8888 /vertex (288 words)

	Graph Concepts (Site not responding. Last check: 2007-10-29)
		When the removal of a single vertex causes a graph to become disconnected, that vertex is called a cut vertex.
		The vertex connectivity of a graph with a cut vertex is always 1.
		A nontrivial connected graph with no cut vertices is called a block.
	home.comcast.net /~lcopes/SciMathMN/concepts/ccut.html (153 words)

	Data Reduction (Site not responding. Last check: 2007-10-29)
		To reject out-of-time events, for pion channels, we look at the difference between event vertex time given by the Start Counter and that given by the RF clock.
		This cut needs to be refined, and the background underneath needs to be examined more carefully.
		If we cut on any rho(3 combinations formed by the 3 pions, the cut is one full width around rho peak, i.e.
	www.jlab.org /~liji/clas_stuff/dataSelection_result.html (433 words)

	Muon Identification Cuts (Site not responding. Last check: 2007-10-29)
		Fiducial stub muon and vertex Z cut are required.
		The set of the rest muon identification cuts are under study.
		Fiducial track, stubless muon which also has the information of energy loss in calorimeter and is not necessary to have hits in muon chamber, vertex Z cut, calorimeter isolation, EM energy cut, and hadronic energy cut are required.
	www.physics.rutgers.edu /~zrwan/thesis/5.4.1/muId_cuts.html (180 words)

	Graph Theory Glossary (Site not responding. Last check: 2007-10-29)
		A circuit is a path which ends at the vertex it begins (so a loop is an circuit of length one).
		A cut vertex is a vertex that if removed (along with all edges incident with it) produces a graph with more connected components than the original graph.
		The vertex a is the initial vertex of the edge and b the terminal vertex.
	www.utm.edu /departments/cens/math/graph/glossary.html (816 words)

	[No title]
		It is not obvious which gen4 cut it failed for pass2 (it was a gen4 pass1 track).
		The three pass1 tracks of gen4 used in the vertex are also pass1 tracks in Gen5 and have similar d0 significance though not identical silicon hits.
		These three tracks no longer formed a signicant vertex (though the lxy significance of the gen4 vtx would have passed the gen5 cut).
	hep.uchicago.edu /~jahred/TMT_QA/moresteve (1342 words)

	[No title]
		DFS(A) Number vertices as they are visited: Num(v) Low(v) the smallest vertex that can be visited from v along 0 or more tree edges terminating with at most one back edge.
		Back edges An articulation node (cut vertex) is a vertex v for which there is a child w with Low(w’) (Num(v) for every node w’ in the subtree with root w.
		The lower the density the less edges it will have (and thus a bigger chance to be disconnected or have cut vertices).
	faculty.washington.edu /moishe/Notes/DFS.doc (212 words)

	Structural and Navigational Analysis of Hypermedia Courseware
		On another hand, cut vertices can be used in a positive manner: they can be considered check points in the courseware, and quizzes can be assigned at such points so that students can confirm whether if they have satisfactorily comprehended the concepts presented in the preceding components.
		When using the Cut Vertex algorithm to analyze a courseware network, the cut vertices in the courseware network must initially be identified; they must then be removed from the courseware.
		When a minimal cut set is identified and the size of the set is small, it is possible that the two knowledge components have only a loose referential relationship to each other.
	www.ewh.ieee.org /soc/es/Nov1998/07/BEGIN.HTM (4858 words)

	GameDev.net - Browsing Game Dictionary (via CobWeb/3.1 planetlab2.tamu.edu) (Site not responding. Last check: 2007-10-29)
		Shader programs, such as vertex and pixel shaders, can be written and compiled in HLSL rather than the various hardware shader assembly languages.
		Rather than using interpolated vertex normals to calculate the lighting data, the normals from from the normal map are used.
		Shaders that affect vertices (vertex shaders) replace the normal transformation and lighting stage of the pipeline, while shaders that affect pixels (pixel shaders), work at the rasterization stage, affecting how the final screen color is determined.
	www.gamedev.net.cob-web.org:8888 /dict/browse.asp?Section=0&CategoryID=7 (8235 words)

	Dr. Dobb's \| Planarity by Edge Addition \| April 1, 2005
		Moreover, the key constraint on this edge addition operation is that any vertex in B must remain on the outside of B if it must be involved in the future embedding of an edge, because new edges are always connected only to the outside of the partial embedding G~.
		Each biconnected component has a "root" vertex that has the least depth-first index in the biconnected component, and is the cut vertex separating the biconnected component's vertices from DFS ancestors of the root.
		A cut vertex is represented by a virtual vertex in each biconnected component for which it is the root, and by a nonvirtual vertex in the biconnected component in which it does not have the least depth-first index.
	www.ddj.com /184406070 (2583 words)

	Agie :: Products :: Wire Cut EDM Systems :: Agiecut Vertex (Site not responding. Last check: 2007-10-29)
		The Agiecut™ Vertex™ is the result of careful review of the requirements of our most discriminating customers.
		Engineered from the ground up for maximum accuracy, the Vertex incorporates compact monoblock construction, vibration dampening, robust components, wire guides close to the workzone, separation of the X and Y Axis, and patented thermal control of all sources of heat.
		To make money cutting these parts, you need to be able to cut with fine wire for long periods of time.
	www.agieus.com /products/wirecut/vertex.asp (363 words)

	Gentler: a tool for systematic web authoringSupporting usability analysis
		Graph theory identifies many interesting classes of vertex, such as median, central and cut-vertex (or hinge).
		If we measure the distance from a page to each of the other pages, and sum this distance, then the pages with minimum total distance are the median pages.
		For different sorts of task, different sorts of vertex might be of interest to the document author or reader; in many cases, the identification of the interesting pages is then a routine application of mathematical analysis.
	ijhcs.open.ac.uk /thimbleby/thimbleby-09.html (1323 words)

	Graph Theory Lecture Notes 8a
		The vertex connectivity of a connected graph G, denoted
		Replacing a vertex v with degree at least 4 by two new vertices v
		, joined by a new edge; each vertex that was adjacent to v in G is joined by an edge to exactly one of v
	www-math.cudenver.edu /~wcherowi/courses/m4408/gtaln8.html (448 words)

	[No title] (Site not responding. Last check: 2007-10-29)
		etr_hist execute user set on user hist set cut user report 2000 exec vertex set on vertex vtx2 err2 secint prim sec set cut vertex prong 5 set cut vertex vtxd 4.0 set cut vertex vtx2 9.0 set off vertex secint exec recon set on recon hist vtuple vtup1 vtup2 vtup3 vtup4 vtup5 strip2 !
		pass11_11_v1 set cut recon cand_csec 5.0 set cut recon cand_cpri 5.0 in ds_defaults.cmd in v0_defaults.cmd disk in reset disk in temp0 disk out out1 strip1 disk out out2 strip2 ocs sets out mag_par !
		change cut vtx2 from 5 to 9 as suggested by russ !
	home.fnal.gov /~syjun/pass2_1_cmd (271 words)

	CS141 BB: ClassS04CS141/Review
		How can you tell whether a vertex is a cut vertex by looking at the low numbers?
		Draw a directed acyclic graph with 10 vertices, choose a source vertex, and label each vertex with the number of paths from the source to that vertex.
		Prove that the root vertex of the DFS tree is a cut vertex iff it has more than one child in the DFS tree
	www.cs.ucr.edu /~neal/2004/cs141/index.cgi?ClassS04CS141/Review (823 words)

	GSLT and vertex cut (Site not responding. Last check: 2007-10-29)
		Effect of a combination of a TLT vertex cut (simulating an MVD vertex cut) and the present GSLT veto
		What is the effect of high-Et cuts on the effect of the present GSLT and how could a MVD-SLT cut help?
		a tight vertex cut becomes more effective at high energies and helps to reduce the rate with about a factor two to three!
	www-zeus.desy.de /~wiggers/vertex_cut.html (138 words)

	minimum vertex cut (Site not responding. Last check: 2007-10-29)
		Definition: The smallest set of vertices in an undirected graph which separate two distinct vertices.
		That is, every path between them passes through some member of the cut.
		Paul E. Black, "minimum vertex cut", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology.
	www.nist.gov /dads/HTML/minvertexcut.html (87 words)

	Yaesu - Vertex Two Way Radio Batteries, Yaesu - Vertex Two Way Radio Battery Packs from CutRateBatteries.com (Site not responding. Last check: 2007-10-29)
		Neither you nor your friends will receive any additional emails from us as a result of using this tool.
		Yaesu - Vertex two way radio batteries are designed to be fully compatible with the original equipment.
		Yaesu - Vertex two way radio battery pack or brand and model number you are currently using from the list below.
	www.cutratebatteries.com /yaesu-vertex-m-12.html (258 words)

	cut vertex (Site not responding. Last check: 2007-10-29)
		Definition: A vertex whose deletion along with incident edges results in a graph with more components than the original graph.
		Note: After Algorithms and Theory of Computation Handbook, page 6-6, Copyright © 1999 by CRC Press LLC.
		Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "cut vertex", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology.
	www.nist.gov /dads/HTML/cutvertex.html (127 words)

	[No title]
		2) Have each participant draw 3 large triangles using a straightedge, and then cut the 3 triangles out.
		By tearing, you can still determine which was the vertex.
		It will be the cut part.) 4) The participants should draw a dot on the page and a straight line through the dot.
	www.pen.k12.va.us /VDOE/Instruction/Elem_M/midgeo3.doc (835 words)

	MINCE (MIN Cut Etc.)
		Other related objectives are cut-width/bandwidth, total (or average) cut, etc. Recursive min-cut bisection tends to return solutions that are simultaneously good with respect to many of these objectives.
		This page offers a leading-edge generic implementation of such vertex reordering and a specific application to variable re-orderings for the Boolean Satisfiability (SAT) problem and Binary Decision Diagrams (BDDs) (the MINCE heuristic).
		Check out the structure of the hole7.cnf instance from the pigeon-hole family: [
	www.eecs.umich.edu /~faloul/Tools/mince (214 words)

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