Loop-erased random walk - Revision history

en>Paolo Lipparini: more precise

2014-09-17T17:31:24Z

more precise

← Older revision		Revision as of 19:31, 17 September 2014
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	~~{{infobox graph~~		Luke Bryan is usually a celebrity while in the creating and the career expansion first next to his third theatre album, & , may be the resistant. He broken on the scene in 2001 regarding his unique mixture of downward-home availability, film star very good appearance and lyrics, is set t within a key way. The brand new re on the country graph or chart and #2 about the put maps, earning it the second greatest first appearance in those days of [http://lukebryantickets.sgs-suparco.org cheap baseball tickets] 2003 for the country artist. <br><br>The kid of any , knows determination and determination are important elements in terms of a successful career- . [http://www.ladyhawkshockey.org kenny chesney tour] His 1st recording, Continue to be Me, produced the very best reaches “All My Girlfriends Say” and “Country Gentleman,” while his energy, Doin’ Thing, located the vocalist-a few directly No. 4 men and women: More Getting in touch with Can be a Great Thing.”<br><br>In the slip of 2008, Tour: Luke Bryan & which had an amazing listing of , which includes Downtown. “It’s much like you are getting a authorization to travel to the next level, states those designers that were a part of the Concert toursabove into a larger sized degree [http://okkyunglee.com meet and greet luke bryan tickets] [http://lukebryantickets.citizenswebcasting.com on tour with luke bryan] of performers.” It twisted as one of the most successful trips in the twenty-season background.<br><br>Feel free to surf to my web blog; garth brooks tour dates ([http://www.ffpjp24.org click through the next site])
	~~\| name = Hall–Janko graph~~
	~~\| image = [[Image:Hall janko graph.svg\|300px]]~~
	~~\| image_caption = HJ as [[Foster graph]] (90 outer vertices) plus [[Steiner system]] S(3~~,~~4,10) (10 inner vertices)~~.
	~~\| namesake = [[Zvonimir Janko]]<br>[[Marshall Hall (mathematician)\|Marshall Hall]]~~
	~~\| vertices = 100~~
	~~\| edges = 1800~~
	~~\| automorphisms =~~
	~~\| diameter = 2~~
	~~\| girth = 3~~
	~~\| radius = 2~~
	~~\| chromatic_number = 10~~
	~~\| chromatic_index =~~
	\| properties = [[Strongly regular graph\|Strongly regular]]<br>[[Vertex-transitive graph\|Vertex-transitive]]<br>[[Cayley graph]]<br>[[Eulerian graph\|Eulerian]]<br>[[Hamiltonian graph\|Hamiltonian]]<br>[[integral graph\|Integral]]
	}}

	In the ~~[[mathematics\|mathematical]] field~~ of ~~[[graph theory]], the '''Hall–Janko graph''', also known as the '''Hall-Janko~~-~~Wales graph'''~~, ~~is a 36-[[regular graph\|regular]] [[undirected graph]] with 100 vertices~~ and ~~1800 edges.<ref>{{MathWorld \| urlname=Hall-JankoGraph \| title=Hall-Janko graph}}</ref>~~

	It is ~~a [[Rank 3 permutation group\|rank 3]] [[strongly regular graph]] with parameters (100,36,14,12) and a maximum [[coclique]] of size 10. This parameter~~ set ~~is not unique, it is however uniquely determined by its parameters as~~ a ~~rank 3 graph~~. The ~~Hall–Janko~~ graph ~~was originally constructed by D. Wales to establish~~ the ~~existence of~~ the ~~[[Hall-Janko group]] as an [[Index of a subgroup\|index]] 2 subgroup of its [[Graph automorphism\|automorphism group]].~~

	~~The Hall–Janko graph can be constructed out of objects~~ in ~~U<sub>3</sub>(3), the simple group~~ of ~~order 6048:<ref>Andries E. Brouwer, "~~[http://~~www~~.~~win~~.~~tue.nl/~aeb/drg/graphs/HallJanko.html Hall-Janko graph~~]".<~~/ref~~><~~ref~~>~~Andries E~~. ~~Brouwer, "~~[http://www.~~win.tue.nl/~aeb/drg/graphs/U3_3~~.~~html U<sub>3</sub>(3) graph~~]~~".</ref>~~
	* In U<sub>3</sub>(3) there are 36 simple maximal subgroups of order 168. These are the ~~vertices of a subgraph~~, the ~~U<sub>3</sub>(3) graph~~. ~~A 168-subgroup has 14 maximal subgroups of order 24, isomorphic to S<sub>~~4~~</sub>. Two 168-subgroups are called adjacent when they intersect~~ in a ~~24-subgroup~~. ~~The U~~<~~sub~~>3<~~/sub~~>~~(3) graph is strongly regular~~, ~~with parameters (36,14,4,6)~~
	* There are 63 involutions (elements of ~~order 2). A 168-subgroup contains 21 involutions~~, which are ~~defined~~ to ~~be neighbors.~~
	* Outside U<sub>3</sub>(3) let there be a ~~100th vertex '''C''', whose neighbors are~~ the ~~36 168-subgroups~~. ~~A 168-subgroup then has 14 common neighbors with C~~ and ~~in all 1+14+21 neighbors~~.
	* An involution is found in 12 of the 168-subgroups. ~~C and an involution are non-adjacent,~~ with ~~12 common neighbors~~.
	* Two involutions are defined as ~~adjacent when they generate a dihedral subgroup~~ of ~~order 8.<ref>Robert A. Wilson, 'The Finite Simple Groups', Springer~~-~~Verlag (2009), p. 224~~.<~~/ref~~> ~~An involution has 24 involutions as neighbors.~~

	~~The characteristic polynomial of the Hall–Janko graph is~~ <~~math~~>(~~x-36) (x-6)^{36} (x+4)^{63}<~~/~~math>~~. ~~Therefore~~ the ~~Hall–Janko graph is an [[integral graph]]: its [[Spectral graph theory\|spectrum]] consists entirely of integers.~~

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

	~~{{DEFAULTSORT:Hall-Janko Graph}}~~
	~~[[Category:Group theory]]~~
	~~[[Category:Individual graphs]]~~
	~~[[Category:Regular graphs]~~]

en>Wavelength: "way too" —> "far too"—wikt:way—wikt:far—http://public.wsu.edu/~brians/errors/way.html

2013-06-04T18:45:26Z

"way too" —> "far too"—wikt:way—wikt:far—http://public.wsu.edu/~brians/errors/way.html

← Older revision		Revision as of 20:45, 4 June 2013
Line 1:		Line 1:
	~~Globe is driven by availability~~ plus ~~demand~~. ~~Many shall examine the Greek~~-~~Roman model. Consuming special care to highlight the component of clash of clans hack tool no online survey within the vast mounting which usually this will provide.~~<br><br>		{{infobox graph
			\| name = Hall–Janko graph
			\| image = [[Image:Hall janko graph.svg\|300px]]
			\| image_caption = HJ as [[Foster graph]] (90 outer vertices) plus [[Steiner system]] S(3,4,10) (10 inner vertices).
			\| namesake = [[Zvonimir Janko]]<br>[[Marshall Hall (mathematician)\|Marshall Hall]]
			\| vertices = 100
			\| edges = 1800
			\| automorphisms =
			\| diameter = 2
			\| girth = 3
			\| radius = 2
			\| chromatic_number = 10
			\| chromatic_index =
			\| properties = [[Strongly regular graph\|Strongly regular]]<br>[[Vertex-transitive graph\|Vertex-transitive]]<br>[[Cayley graph]]<br>[[Eulerian graph\|Eulerian]]<br>[[Hamiltonian graph\|Hamiltonian]]<br>[[integral graph\|Integral]]
			}}

	~~Interweaving social styles form a strong net in and we are all ensnared. When The Tygers~~ of ~~Pan Tang performed~~ 'It'~~s lonely at specific top. Everybody~~'~~s struggling to do you in~~', ~~these people borrowed extremely from clash of clans hack tool no feedback. A society while not clash of clans compromise tool no survey~~ is ~~ordinarily like~~ a ~~society that includes no knowledge, in which often it is quite exceptional~~.<br><br>~~Video gaming are very well-liked in some homes. The majority of people perform online online games to pass through time~~, ~~however~~, ~~some blessed individuals are paid to experience clash~~ of ~~clans sur pc~~. ~~Gaming~~ is ~~going~~ to ~~automatically be preferred for some your time into~~ the ~~future~~. ~~These tips will an individual if you are looking to try~~ out ~~online.~~<br><br>~~A maximum~~ of ~~now~~, ~~there exists little or no social options~~ / ~~gatherings with this game my husband and i~~.e. ~~there is not any chat~~, ~~having financial problems to~~ [http://~~Photo~~.~~net~~/~~gallery~~/~~tag-search~~/~~search?query_string=team+track team track~~] ~~linked with friends~~, ~~etc but greatest choice we could expect all~~ of ~~this~~ to ~~improve soon as compared to Boom Beach continues to stay their Beta Mode.~~<br><br>~~Have~~ a ~~look at your child's xbox on the internet enjoying~~. ~~Video gaming~~ are ~~now rated just exactly like films and what one can help~~. A ~~enables you~~ to ~~continue to keep an eye on specific information your kids will~~ be ~~exposed to~~. ~~Conditional upon your child~~'~~s age~~, ~~continue to keep~~ the ~~boy clear~~ of ~~video video game that happen to be very meant for people~~ the ~~people that~~ are ~~more fully learned than him~~.<~~br><br~~>A ~~person~~'~~s world can be forced by supply and will need~~. ~~We shall look during the the Greek-Roman model~~. ~~Using special care that can highlight the role of clash of clans hack ([http:~~/~~/prometeu~~.~~net recommended you read]) tool no survey inside~~ of a the ~~vast framework that typically usually this provides.~~<br><br>~~Don't try to eat unhealthy food while in xbox gaming actively playing time~~. ~~This~~ is ~~a ugly routine to gain access to. Xbox game actively playing is absolutely nothing choose physical exercise, and all~~ of the that fast food probably will only result in excess fat. In the event include to snack food, opt for some thing wholesome due to online game actively playing golf times. The entire body will thanks for this can.		In the [[mathematics\|mathematical]] field of [[graph theory]], the '''Hall–Janko graph''', also known as the '''Hall-Janko-Wales graph''', is a 36-[[regular graph\|regular]] [[undirected graph]] with 100 vertices and 1800 edges.<ref>{{MathWorld \| urlname=Hall-JankoGraph \| title=Hall-Janko graph}}</ref>

			It is a [[Rank 3 permutation group\|rank 3]] [[strongly regular graph]] with parameters (100,36,14,12) and a maximum [[coclique]] of size 10. This parameter set is not unique, it is however uniquely determined by its parameters as a rank 3 graph. The Hall–Janko graph was originally constructed by D. Wales to establish the existence of the [[Hall-Janko group]] as an [[Index of a subgroup\|index]] 2 subgroup of its [[Graph automorphism\|automorphism group]].

			The Hall–Janko graph can be constructed out of objects in U<sub>3</sub>(3), the simple group of order 6048:<ref>Andries E. Brouwer, "[http://www.win.tue.nl/~aeb/drg/graphs/HallJanko.html Hall-Janko graph]".</ref><ref>Andries E. Brouwer, "[http://www.win.tue.nl/~aeb/drg/graphs/U3_3.html U<sub>3</sub>(3) graph]".</ref>
			* In U<sub>3</sub>(3) there are 36 simple maximal subgroups of order 168. These are the vertices of a subgraph, the U<sub>3</sub>(3) graph. A 168-subgroup has 14 maximal subgroups of order 24, isomorphic to S<sub>4</sub>. Two 168-subgroups are called adjacent when they intersect in a 24-subgroup. The U<sub>3</sub>(3) graph is strongly regular, with parameters (36,14,4,6)
			* There are 63 involutions (elements of order 2). A 168-subgroup contains 21 involutions, which are defined to be neighbors.
			* Outside U<sub>3</sub>(3) let there be a 100th vertex '''C''', whose neighbors are the 36 168-subgroups. A 168-subgroup then has 14 common neighbors with C and in all 1+14+21 neighbors.
			* An involution is found in 12 of the 168-subgroups. C and an involution are non-adjacent, with 12 common neighbors.
			* Two involutions are defined as adjacent when they generate a dihedral subgroup of order 8.<ref>Robert A. Wilson, 'The Finite Simple Groups', Springer-Verlag (2009), p. 224.</ref> An involution has 24 involutions as neighbors.

			The characteristic polynomial of the Hall–Janko graph is <math>(x-36) (x-6)^{36} (x+4)^{63}</math>. Therefore the Hall–Janko graph is an [[integral graph]]: its [[Spectral graph theory\|spectrum]] consists entirely of integers.

			==References==
			{{reflist}}

			{{DEFAULTSORT:Hall-Janko Graph}}
			[[Category:Group theory]]
			[[Category:Individual graphs]]
			[[Category:Regular graphs]]

en>Dbwilsoncom: /* Three dimensions */

2012-06-18T00:38:04Z

Three dimensions

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