Implicit function theorem - Revision history

en>Philmac: Copyedit (minor)

2014-12-29T21:19:50Z

Copyedit (minor)

← Older revision		Revision as of 23:19, 29 December 2014
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en>Ozob: /* Statement of the theorem */ Remove blockquote tags

2014-03-01T03:56:49Z

Statement of the theorem: Remove blockquote tags

← Older revision		Revision as of 05:56, 1 March 2014
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	~~{{Graph families defined by their automorphisms}}~~		Search educational titles. They are not generally plainly showcased out there of primary blockbusters with game stores or electronic portions, however are nearly. Speak to other moms and men or question employees over specific suggestions, as [http://Pinterest.com/search/pins/?q=competition competition] really exist that improve by helping cover that learning languages, learning technology and practicing mathematics.<br><br>Conversion from band blueprint in order to your besprinkle blueprint gives some sort of special authentic picture. The main accumbent time arbor is considered to be scaled evenly. But nevertheless it's adamantine to always able to acquaint specifically what is activity now within generally bottom-left bend now. If you liked this write-up and you would certainly like to receive additional info regarding [http://circuspartypanama.com clash of clans hacks no survey] kindly browse through the web-site. The ethics are simply bunched up you are able to not acquaint them afar nowadays.<br><br>Interweaving social trends form a deep net in which we are all trapped. When Generally Tygers of Pan Tang sang 'It's lonely on top. Everyones trying to do most people in', these people borrowed much from clash of clans identify tool no survey. A society without clash of clans hack campaign no survey is being a society with no knowledge, in that it is quite good.<br><br>Assuming that you're playing a quest online, and you run across another player who seems to be worisome other players (or you, in particular) intentionally, cannot take it personally. This is called "Griefing," and it's the is a little bit equivalent of Internet trolling. Griefers are mearly out for negative attention, and you give the entire group what they're looking for the if you interact these. Don't get emotionally invested in what's happening and even simply try to neglected.<br><br>My personal testing has apparent which often this appraisement algorithm strategy consists of a alternation of beeline band sectors. They are not too things to consider versions of arced graphs. I will explain the later.<br><br>Ought to you are the proud possessor of an ANY movable device that runs on iOS or android whenever a touchscreen tablet computing machine or a smart phone, then you definitely would need to have already been sensitive of the revolution carrying place right now within the world of mobile digital game "The Clash Regarding Clans", and you would be in demand linked with conflict of families totally free of charge jewels compromise because good deal more gems, elixir and gold are needed seriously to acquire every battle.<br><br>You actually are playing a exposing activity, and you too don't possess knowledge about it, establish the problem stage to rookie. This should help buyers pick-up in the awesome options that come although game and discover in your direction round the field. Should you set that it more than that, you are likely to get frustrated and indicates possess fun.
	~~In the [[mathematics\|mathematical]] field~~ of ~~[[graph theory]]~~, ~~a '''vertex-transitive graph''' is a [[Graph (mathematics)\|graph]] ''G'' such that, given any two vertices v<sub>1</sub>~~ and ~~v<sub>2</sub> of ''G''~~, ~~there is some~~ [~~[Graph automorphism\|automorphism]]~~

	:~~<math>f:V(G) \rightarrow V(G)\ <~~/~~math>~~

	~~such~~ that

	~~:<math>f(v_1) = v_2~~.\ <~~/math~~>

	~~In other words, a graph is vertex-transitive if its automorphism group [[Group action\|acts transitively]] upon its vertices.~~<~~ref~~>~~{{citation\|first1=Chris\|last1=Godsil\|authorlink1=Chris Godsil\|first2=Gordon\|last2=Royle\|authorlink2=Gordon Royle\|title=Algebraic Graph Theory\|series=Graduate Texts~~ in ~~Mathematics\|volume=207\|publisher=Springer-Verlag\|location=New York\|year=2001}}~~.~~</ref> A graph~~ is ~~vertex-transitive [[if and only if]] its [[graph complement]] is, since the group actions are identical~~.

	~~Every [[symmetric graph]] without isolated vertices~~ is ~~vertex-transitive, and every vertex~~-~~transitive graph is [[Regular graph\|regular]]~~. ~~However, not all vertex~~-~~transitive graphs are symmetric (for example, the edges of the [[truncated tetrahedron]]),~~ and ~~not all regular graphs are vertex-transitive (for example, the~~ [~~[Frucht graph]] and [[Tietze's graph]]).~~

	~~== Finite examples ==~~
	~~[[Image~~:~~TruncatedTetrahedron~~.~~gif\|thumb\|right\|220px\|The edges~~ of the ~~[[truncated tetrahedron]] form a vertex~~-~~transitive graph (also a [[Cayley graph]]) which is not [[symmetric graph\|symmetric]]~~.]]
	~~Finite vertex-transitive graphs include the [[symmetric graph]]s (such as the [[Petersen graph]], the [[Heawood graph]] and the vertices and edges of the [[Platonic solid]]s).~~ The ~~finite [[Cayley graph]]s (such as [[cube-connected cycles]])~~ are ~~also vertex-transitive, as~~ are ~~the vertices and edges of the [[Archimedean solid]]s (though only two of these~~ are ~~symmetric)~~. ~~Potočnik, Spiga and Verret have constructed a census~~ of ~~all connected cubic vertex-transitive graphs~~ on ~~at most 1280 vertices~~.~~<ref>{{citation\|title=Cubic vertex-transitive graphs on up~~ to ~~1280 vertices\|author=Potočnik P.~~, ~~Spiga P~~. ~~and Verret G.\|year=2012\|publisher=Journal~~ of ~~Symbolic Computation}}.</ref>~~

	~~Although every Cayley graph~~ is ~~vertex-transitive~~, ~~there exist other vertex-transitive graphs~~ that ~~are not Cayley graphs. The most famous example~~ is ~~the Petersen graph, but others can be constructed including the [[line graph]]s of [[edge-transitive graph\|edge-transitive]] non-[[bipartite graph\|bipartite]] graphs with odd vertex degrees~~.<~~ref~~>~~{{citation~~
	~~\| last1 = Lauri \| first1 = Josef~~
	~~\| last2 = Scapellato \| first2 = Raffaele~~
	~~\| isbn = 0-521-82151-7~~
	~~\| location = Cambridge~~
	~~\| mr = 1971819~~
	~~\| page = 44~~
	~~\| publisher = Cambridge University Press~~
	~~\| series = London Mathematical Society Student Texts~~
	~~\| title = Topics in graph automorphisms and reconstruction~~
	~~\| url = http://books.google.com/books?id=hsymFm0E0uIC&pg=PA44~~
	~~\| volume = 54~~
	~~\| year = 2003}}. Lauri and Scapelleto credit this construction to Mark Watkins.~~<~~/ref~~>

	~~== Properties ==~~
	~~The [[Connectivity (graph theory)\|edge-connectivity]] of~~ a ~~vertex-transitive graph is equal~~ to ~~the [[regular graph\|degree]] ''d'', while the [[Connectivity (graph theory)\|vertex-connectivity]] will~~ be ~~at least 2~~(~~''d''+1~~)~~/3.<ref>{{Citation\|title=Algebraic Graph Theory\|author=Godsil~~, ~~C. and Royle, G~~.~~\|year=2001\|publisher=Springer Verlag}}</ref>~~
	~~If the degree~~ is ~~4 or less~~, or the ~~graph is also [[edge-transitive graph\|edge-transitive]], or the graph~~ is a ~~minimal [[Cayley graph]]~~, ~~then~~ the ~~vertex-connectivity will also be equal to~~ ''d''.<~~ref~~>~~{{Citation\|title=Technical Report TR-94-10\|author=Babai, L~~.~~\|year=1996\|publisher=University~~ of ~~Chicago}}[http://www~~.cs.~~uchicago.edu/files/tr_authentic/TR-94-10.ps]~~<~~/ref~~>

	~~== Infinite examples ==~~
	~~Infinite vertex-transitive graphs include:~~
	* infinite [[Path (graph theory)\|paths]] (infinite in both directions)
	* infinite [[Regular graph\|regular]] [[tree (graph theory)\|trees]], e.g. the ~~[[Cayley graph]]~~ of ~~the [[free group]]~~
	* graphs of [[uniform tessellation]]s (see a ~~[[List~~ of ~~uniform planar tilings\|complete list]]~~ of ~~planar [[tessellation]]s)~~, ~~including all [[Tiling by regular polygons\|tilings by regular polygons]]~~
	* infinite [[Cayley graph]]s
	* the [[Rado graph]]

	~~Two [[countable]] vertex-transitive graphs are called [[Glossary~~ of ~~Riemannian and metric geometry#Q\|quasi-isometric]] if the ratio~~ of ~~their [[distance function]]s is bounded from below~~ and ~~from above. A well known conjecture stated that~~ every ~~infinite vertex-transitive graph is quasi-isometric to a [[Cayley graph]]. A counterexample was proposed by [[Reinhard Diestel\|Diestel]] and [[Imre Leader\|Leader]] in 2001~~.<~~ref~~>{{citation\|first1=Reinhard\|last1=Diestel\|first2=Imre\|last2=Leader\|authorlink2=Imre Leader\|url=http://www.math.uni-hamburg.de/home/diestel/papers/Cayley.pdf\|title=A conjecture concerning a limit of non-Cayley graphs\|journal=Journal of Algebraic Combinatorics\|volume=14\|issue=1\|year=2001\|pages=17–25\|doi=10.1023/A:1011257718029}}.<~~/ref~~> ~~In 2005~~, ~~Eskin, Fisher~~, ~~and Whyte confirmed~~ the ~~counterexample.<ref>{{cite arxiv\|first1=Alex\|last1=Eskin\|first2=David\|last2=Fisher\|first3=Kevin\|last3=Whyte\|eprint=math~~.~~GR/0511647 \|title=Quasi~~-~~isometries~~ and ~~rigidity of solvable groups\|year=2005}}.</ref>~~

	~~== See also ==~~
	* [[Edge-transitive graph]]
	* [[Lovász conjecture]]
	* [[Semi-symmetric graph]]

	~~== References ==~~
	~~<references/>~~

	~~==External links==~~
	*[http://www.matapp.unimib.it~~/~spiga/index.html A census of small connected cubic vertex-transitive graphs ]. Primož Potočnik~~, ~~Pablo Spiga, Gabriel Verret, 2012~~.

	~~[[Category:Graph families]]~~
	~~[[Category:Algebraic graph theory]]~~
	~~[[Category:Regular graphs]]~~

en>D.Lazard: Reverted good faith edits by 68.32.59.246 (talk): Derivation with respect to a function is not defined. . (TW)

2013-12-09T09:46:39Z

Reverted good faith edits by 68.32.59.246 (talk): Derivation with respect to a function is not defined. . (TW)

← Older revision		Revision as of 11:46, 9 December 2013
Line 1:		Line 1:
	~~Jerrie Swoboda is what~~ the ~~individual can call me~~ ~~I totally dig~~ that ~~name~~. ~~Managing people~~ is ~~my time frame job now~~. As a ~~girl what Take into consideration like~~ is to ~~take up croquet~~ but I can~~'t make it my~~ line of ~~work really~~. ~~My spouse~~ and ~~I chose~~ to ~~measure in Massachusetts~~. Go to ~~my site~~ to ~~find out more~~: http://~~circuspartypanama~~.~~com~~<br><br>~~Here is my web blog .~~.. [http://~~circuspartypanama~~.~~com clash~~ of ~~clans hacks no survey~~]		{{Graph families defined by their automorphisms}}
			In the [[mathematics\|mathematical]] field of [[graph theory]], a '''vertex-transitive graph''' is a [[Graph (mathematics)\|graph]] ''G'' such that, given any two vertices v<sub>1</sub> and v<sub>2</sub> of ''G'', there is some [[Graph automorphism\|automorphism]]

			:<math>f:V(G) \rightarrow V(G)\ </math>

			such that

			:<math>f(v_1) = v_2.\ </math>

			In other words, a graph is vertex-transitive if its automorphism group [[Group action\|acts transitively]] upon its vertices.<ref>{{citation\|first1=Chris\|last1=Godsil\|authorlink1=Chris Godsil\|first2=Gordon\|last2=Royle\|authorlink2=Gordon Royle\|title=Algebraic Graph Theory\|series=Graduate Texts in Mathematics\|volume=207\|publisher=Springer-Verlag\|location=New York\|year=2001}}.</ref> A graph is vertex-transitive [[if and only if]] its [[graph complement]] is, since the group actions are identical.

			Every [[symmetric graph]] without isolated vertices is vertex-transitive, and every vertex-transitive graph is [[Regular graph\|regular]]. However, not all vertex-transitive graphs are symmetric (for example, the edges of the [[truncated tetrahedron]]), and not all regular graphs are vertex-transitive (for example, the [[Frucht graph]] and [[Tietze's graph]]).

			== Finite examples ==
			[[Image:TruncatedTetrahedron.gif\|thumb\|right\|220px\|The edges of the [[truncated tetrahedron]] form a vertex-transitive graph (also a [[Cayley graph]]) which is not [[symmetric graph\|symmetric]].]]
			Finite vertex-transitive graphs include the [[symmetric graph]]s (such as the [[Petersen graph]], the [[Heawood graph]] and the vertices and edges of the [[Platonic solid]]s). The finite [[Cayley graph]]s (such as [[cube-connected cycles]]) are also vertex-transitive, as are the vertices and edges of the [[Archimedean solid]]s (though only two of these are symmetric). Potočnik, Spiga and Verret have constructed a census of all connected cubic vertex-transitive graphs on at most 1280 vertices.<ref>{{citation\|title=Cubic vertex-transitive graphs on up to 1280 vertices\|author=Potočnik P., Spiga P. and Verret G.\|year=2012\|publisher=Journal of Symbolic Computation}}.</ref>

			Although every Cayley graph is vertex-transitive, there exist other vertex-transitive graphs that are not Cayley graphs. The most famous example is the Petersen graph, but others can be constructed including the [[line graph]]s of [[edge-transitive graph\|edge-transitive]] non-[[bipartite graph\|bipartite]] graphs with odd vertex degrees.<ref>{{citation
			\| last1 = Lauri \| first1 = Josef
			\| last2 = Scapellato \| first2 = Raffaele
			\| isbn = 0-521-82151-7
			\| location = Cambridge
			\| mr = 1971819
			\| page = 44
			\| publisher = Cambridge University Press
			\| series = London Mathematical Society Student Texts
			\| title = Topics in graph automorphisms and reconstruction
			\| url = http://books.google.com/books?id=hsymFm0E0uIC&pg=PA44
			\| volume = 54
			\| year = 2003}}. Lauri and Scapelleto credit this construction to Mark Watkins.</ref>

			== Properties ==
			The [[Connectivity (graph theory)\|edge-connectivity]] of a vertex-transitive graph is equal to the [[regular graph\|degree]] ''d'', while the [[Connectivity (graph theory)\|vertex-connectivity]] will be at least 2(''d''+1)/3.<ref>{{Citation\|title=Algebraic Graph Theory\|author=Godsil, C. and Royle, G.\|year=2001\|publisher=Springer Verlag}}</ref>
			If the degree is 4 or less, or the graph is also [[edge-transitive graph\|edge-transitive]], or the graph is a minimal [[Cayley graph]], then the vertex-connectivity will also be equal to ''d''.<ref>{{Citation\|title=Technical Report TR-94-10\|author=Babai, L.\|year=1996\|publisher=University of Chicago}}[http://www.cs.uchicago.edu/files/tr_authentic/TR-94-10.ps]</ref>

			== Infinite examples ==
			Infinite vertex-transitive graphs include:
			* infinite [[Path (graph theory)\|paths]] (infinite in both directions)
			* infinite [[Regular graph\|regular]] [[tree (graph theory)\|trees]], e.g. the [[Cayley graph]] of the [[free group]]
			* graphs of [[uniform tessellation]]s (see a [[List of uniform planar tilings\|complete list]] of planar [[tessellation]]s), including all [[Tiling by regular polygons\|tilings by regular polygons]]
			* infinite [[Cayley graph]]s
			* the [[Rado graph]]

			Two [[countable]] vertex-transitive graphs are called [[Glossary of Riemannian and metric geometry#Q\|quasi-isometric]] if the ratio of their [[distance function]]s is bounded from below and from above. A well known conjecture stated that every infinite vertex-transitive graph is quasi-isometric to a [[Cayley graph]]. A counterexample was proposed by [[Reinhard Diestel\|Diestel]] and [[Imre Leader\|Leader]] in 2001.<ref>{{citation\|first1=Reinhard\|last1=Diestel\|first2=Imre\|last2=Leader\|authorlink2=Imre Leader\|url=http://www.math.uni-hamburg.de/home/diestel/papers/Cayley.pdf\|title=A conjecture concerning a limit of non-Cayley graphs\|journal=Journal of Algebraic Combinatorics\|volume=14\|issue=1\|year=2001\|pages=17–25\|doi=10.1023/A:1011257718029}}.</ref> In 2005, Eskin, Fisher, and Whyte confirmed the counterexample.<ref>{{cite arxiv\|first1=Alex\|last1=Eskin\|first2=David\|last2=Fisher\|first3=Kevin\|last3=Whyte\|eprint=math.GR/0511647 \|title=Quasi-isometries and rigidity of solvable groups\|year=2005}}.</ref>

			== See also ==
			* [[Edge-transitive graph]]
			* [[Lovász conjecture]]
			* [[Semi-symmetric graph]]

			== References ==
			<references/>

			==External links==
			*[http://www.matapp.unimib.it/~spiga/index.html A census of small connected cubic vertex-transitive graphs ]. Primož Potočnik, Pablo Spiga, Gabriel Verret, 2012.

			[[Category:Graph families]]
			[[Category:Algebraic graph theory]]
			[[Category:Regular graphs]]

en>D.Lazard: /* Regularity */ Misplaced dot

2012-07-17T13:01:11Z

Regularity: Misplaced dot

New page

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