Overconstrained mechanism - Revision history

en>Cydebot: Robot - Speedily moving category Linkages to :Category:Linkages (mechanical) per CFDS.

2014-11-11T09:16:25Z

Robot - Speedily moving category Linkages to Category:Linkages (mechanical) per CFDS.

← Older revision		Revision as of 11:16, 11 November 2014
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en>Wavelength: inserting 1 hyphen: —> "three-dimensional"—wikt:three-dimensional

2014-02-25T00:38:11Z

inserting 1 hyphen: —> "three-dimensional"—wikt:three-dimensional

← Older revision		Revision as of 02:38, 25 February 2014
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	~~{{Infobox graph~~		The name of the writer is Numbers. One of the extremely best things in the world for me is to do aerobics and I've been performing it for quite a whilst. Her family members life in Minnesota. Hiring is her day job now and she will not change it whenever quickly.<br><br>My website; home std test kit; [http://www.kindrasdesigns-testing.com/index.php?do=/profile-12578/info/ Related Homepag],
	\| name ~~= Butterfly graph~~
	~~\| image = [[Image:Butterfly graph.svg\|200px]]~~
	~~\| vertices = 5~~
	~~\| edges = 6~~
	~~\| automorphisms = 8 ([[Dihedral group\|''D'']]<sub>4</sub>)~~
	~~\| diameter = 2~~
	~~\| radius = 1~~
	~~\| girth = 3~~
	~~\| chromatic_number = 3~~
	~~\| chromatic_index = 4~~
	~~\| properties = [[planar graph\|Planar]]<br>[[unit distance graph\|Unit distance]]<br>[[Eulerian graph\|Eulerian]]~~
	}}

	~~In the [[mathematics\|mathematical]] field~~ of ~~[[graph theory]], the '''butterfly graph''' (also called~~ the ~~'''bowtie graph''' and the '''hourglass graph''')~~ is ~~a [[planar graph\|planar]] [[undirected graph]] with 5 vertices and 6 edges~~.<ref>{{MathWorld\|urlname=ButterflyGraph\|title=Butterfly Graph}}</ref><ref>ISGCI: Information System on Graph Classes and their Inclusions. "[http://www.graphclasses.org/smallgraphs.html List of Small Graphs]".</ref> It can be constructed by joining 2 copies of the ~~[[cycle graph]] ''C''<sub>3</sub> with a common vertex and~~ is ~~therefore isomorphic~~ to ~~the [[friendship graph]]~~ '~~'F''<sub>2</sub>.~~

	The butterfly Graph has [[graph diameter\|diameter]] 2 and [[girth (graph theory)\|girth]] 3, radius 1, [[chromatic number]] 3, [[chromatic index]] 4 and is both [[Eulerian graph\|Eulerian]] and [[unit distance graph\|unit distance]]. It is also a 1-[[k-vertex-connected graph\|vertex-connected graph]] and a ~~2-[[k-edge-connected graph\|edge-connected graph]]~~.

	~~There are only 3 [[Graceful labeling\|non-graceful]] simple graphs with five vertices~~. ~~One of them~~ is ~~the butterfly graph. The two others are [[cycle graph]] ''C''<sub>5</sub>~~ and ~~the [[complete graph]] ''K''<sub>5</sub>~~.<~~ref name="Mat2007"~~>~~{{mathworld\|title=Graceful graph\|urlname=GracefulGraph}}~~<~~/ref~~>

	~~==Bowtie-free graphs==~~
	~~A graph is '''bowtie-free''' if it has no butterfly as an [[induced subgraph]]. The [[triangle-free graph]]s are bowtie-free graphs, since every butterfly contains a triangle.~~

	In a [[k-vertex-connected graph\|''k''-vertex-connected]] graph, and edge is said ''k''-contractible if the contraction of the edge results in a ''k''-connected graph. Ando, Kaneko, Kawarabayashi and Yoshimoto proved that every ''k''-vertex-connected bowtie-free graph has a ''k''-contractible edge.<ref>Kiyoshi Ando "Contractible Edges in a k-Connected Graph", CJCDGCGT 2005: 10-20 [http://www.~~combinatorics~~.~~net~~/~~conf/conf/abstract/ando~~.~~htm].</ref>~~

	~~==Algebraic properties=~~=
	~~The full automorphism group of the butterfly graph is a group of order 8 isomorphic to the [[Dihedral group]] ''D''<sub>4<~~/~~sub>, the group of symmetries of a [[Square (geometry)\|square]], including both rotations and reflections.~~

	~~The [[characteristic polynomial]] of the butterfly graph is <math>~~-~~(x-1)(x+1)^2(x^2-x-4)<~~/~~math>.~~

	~~== References ==~~
	~~{{reflist}}~~

	~~[[Category:Individual graphs]]~~
	~~[[Category:Planar graphs]~~]

en>Simiprof: added Watt II based overconstrained mechanisms animated GIFs

2013-12-31T01:21:18Z

added Watt II based overconstrained mechanisms animated GIFs

← Older revision		Revision as of 03:21, 31 December 2013
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	~~Marvella is what you can call her but it~~'~~s not~~ the ~~most feminine~~ title ~~out there~~. ~~One~~ of the ~~very very best issues in the world for him~~ is to ~~collect badges but he~~ is ~~struggling to discover time for it~~. ~~Puerto Rico~~ is ~~exactly where he's been living for years~~ and ~~he will never move~~. ~~Bookkeeping~~ is ~~what I do~~.<br><br>~~My weblog~~ ... [http://www.~~alhuloul~~.~~com~~/?p=~~235037 www~~.~~alhuloul~~.~~com~~]		{{Infobox graph
			\| name = Butterfly graph
			\| image = [[Image:Butterfly graph.svg\|200px]]
			\| vertices = 5
			\| edges = 6
			\| automorphisms = 8 ([[Dihedral group\|''D'']]<sub>4</sub>)
			\| diameter = 2
			\| radius = 1
			\| girth = 3
			\| chromatic_number = 3
			\| chromatic_index = 4
			\| properties = [[planar graph\|Planar]]<br>[[unit distance graph\|Unit distance]]<br>[[Eulerian graph\|Eulerian]]
			}}

			In the [[mathematics\|mathematical]] field of [[graph theory]], the '''butterfly graph''' (also called the '''bowtie graph''' and the '''hourglass graph''') is a [[planar graph\|planar]] [[undirected graph]] with 5 vertices and 6 edges.<ref>{{MathWorld\|urlname=ButterflyGraph\|title=Butterfly Graph}}</ref><ref>ISGCI: Information System on Graph Classes and their Inclusions. "[http://www.graphclasses.org/smallgraphs.html List of Small Graphs]".</ref> It can be constructed by joining 2 copies of the [[cycle graph]] ''C''<sub>3</sub> with a common vertex and is therefore isomorphic to the [[friendship graph]] ''F''<sub>2</sub>.

			The butterfly Graph has [[graph diameter\|diameter]] 2 and [[girth (graph theory)\|girth]] 3, radius 1, [[chromatic number]] 3, [[chromatic index]] 4 and is both [[Eulerian graph\|Eulerian]] and [[unit distance graph\|unit distance]]. It is also a 1-[[k-vertex-connected graph\|vertex-connected graph]] and a 2-[[k-edge-connected graph\|edge-connected graph]].

			There are only 3 [[Graceful labeling\|non-graceful]] simple graphs with five vertices. One of them is the butterfly graph. The two others are [[cycle graph]] ''C''<sub>5</sub> and the [[complete graph]] ''K''<sub>5</sub>.<ref name="Mat2007">{{mathworld\|title=Graceful graph\|urlname=GracefulGraph}}</ref>

			==Bowtie-free graphs==
			A graph is '''bowtie-free''' if it has no butterfly as an [[induced subgraph]]. The [[triangle-free graph]]s are bowtie-free graphs, since every butterfly contains a triangle.

			In a [[k-vertex-connected graph\|''k''-vertex-connected]] graph, and edge is said ''k''-contractible if the contraction of the edge results in a ''k''-connected graph. Ando, Kaneko, Kawarabayashi and Yoshimoto proved that every ''k''-vertex-connected bowtie-free graph has a ''k''-contractible edge.<ref>Kiyoshi Ando "Contractible Edges in a k-Connected Graph", CJCDGCGT 2005: 10-20 [http://www.combinatorics.net/conf/conf/abstract/ando.htm].</ref>

			==Algebraic properties==
			The full automorphism group of the butterfly graph is a group of order 8 isomorphic to the [[Dihedral group]] ''D''<sub>4</sub>, the group of symmetries of a [[Square (geometry)\|square]], including both rotations and reflections.

			The [[characteristic polynomial]] of the butterfly graph is <math>-(x-1)(x+1)^2(x^2-x-4)</math>.

			== References ==
			{{reflist}}

			[[Category:Individual graphs]]
			[[Category:Planar graphs]]

en>Lannm: Fixed broken link URL

2012-04-04T16:07:44Z

Fixed broken link URL

New page

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