Samuelson's inequality - Revision history

2601:2:4D00:27B:9DCF:32C0:8000:A68F: punctuation corrections required by WP:MOS

2014-08-10T23:59:19Z

punctuation corrections required by WP:MOS

← Older revision		Revision as of 01:59, 11 August 2014
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	~~{{infobox graph~~		The main advantage of using the blog is that anyone can use the Word - Press blog and customize the elements in the theme regardless to limited knowledge about internet and website development. You can either install Word - Press yourself or use free services offered on the web today. A pinch of tablet centric strategy can get your Word - Press site miles ahead of your competitors, so here are few strategies that will give your Wordpress websites and blogs an edge over your competitors:. s and intelligently including a substantial amount of key words in the title tags, image links, etc. provided by Word - Press Automatic Upgrade, so whenever you need to update the new version does not, it automatically creates no webmaster. <br><br>Right starting from social media support to search engine optimization, such plugins are easily available within the Word - Press open source platform. The higher your blog ranks on search engines, the more likely people will find your online marketing site. There are number of web services that offer Word press development across the world. Furthermore, with the launch of Windows 7 Phone is the smart phone market nascent App. W3C compliant HTML and a good open source powered by Word - Press CMS site is regarded as the prime minister. <br><br>Saying that, despite the launch of Wordpress Express many months ago, there has still been no sign of a Wordpress video tutorial on offer UNTIL NOW. Browse through the popular Wordpress theme clubs like the Elegant Themes, Studio Press, Woo - Themes, Rocket Theme, Simple Themes and many more. Use this section to change many formatting elements. These frequent updates have created menace in the task of optimization. After that the developer adds the unordered list for navigations. <br><br>You can add keywords but it is best to leave this alone. I have compiled a few tips on how you can start a food blog and hopefully the following information and tips can help you to get started on your food blogging creative journey. Enterprise, when they plan to hire Word - Press developer resources still PHP, My - SQL and watch with great expertise in codebase. In the event you loved this information and you would want to receive more information with regards to [http://ll.my/wordpressdropboxbackup792091 wordpress backup] kindly visit the web-page. Contact Infertility Clinic Providing One stop Fertility Solutions at:. Make sure you have the latest versions of all your plugins are updated. <br><br>Website security has become a major concern among individuals all over the world. Automated deal feed integration option to populate your blog with relevant deals. However, you must also manually approve or reject comments so that your website does not promote parasitic behavior. Page speed is an important factor in ranking, especially with Google. Get started today so that people searching for your type of business will be directed to you.
	~~\| name = Robertson graph~~
	~~\| image = [[Image:Robertson graph hamiltonian.svg\|240px]]~~
	~~\| image_caption =~~ The ~~Robertson graph~~ is ~~Hamiltonian~~.
	~~\| namesake = [[Neil Robertson (mathematician)\|Neil Robertson]]~~
	~~\| vertices = 19~~
	~~\| edges = 38~~
	~~\| automorphisms = 24 ([[dihedral group\|D<sub>12</sub>]])~~
	~~\| girth = 5~~
	~~\| diameter = 3~~
	~~\| radius = 3~~
	~~\| chromatic_number = 3~~
	~~\| chromatic_index = 5<ref>{{MathWorld\|urlname=Class2Graph\|title=Class 2 Graph}}</ref>~~
	~~\| properties = [[Cage (graph theory)\|Cage]]<br>[[Hamiltonian graph\|Hamiltonian]]~~
	}}
	In the ~~[[mathematics\|mathematical]] field~~ of ~~[[graph theory]]~~, the ~~'''Robertson graph''' or '''(4~~,5)-~~cage~~,~~''' is a 4-[[regular graph\|regular]] [[undirected graph]] with 19 vertices and 38 edges named after [[Neil Robertson (mathematician)\|Neil Robertson]]~~.<~~ref~~>~~{{MathWorld\|urlname=RobertsonGraph\|title=Robertson Graph}}~~<~~/ref~~>~~<ref>Bondy~~, J. ~~A. and Murty~~, U. S. ~~R. Graph Theory~~ with ~~Applications. New York: North Holland, p. 237, 1976.</ref>~~

	~~The Robertson graph~~ is the ~~unique [[cage graph\|(4,5)-cage graph]]~~ and ~~was discovered~~ by ~~Robertson in 1964~~.<~~ref~~>~~Robertson~~, N. ~~"The Smallest Graph of Girth 5~~ and ~~Valency 4~~.~~" Bull~~. ~~Amer~~. ~~Math. Soc. 70, 824-825, 1964~~.<~~/ref~~> ~~As a cage graph,~~ it is the ~~smallest 4-regular graph with girth 5~~.

	~~It has [[chromatic number]] 3~~, ~~[[chromatic index]] 5~~, ~~diameter 3, radius 3 and is both 4-[[k~~-~~vertex-connected graph\|vertex-connected]]~~ and ~~4-[[k-edge-connected graph\|edge-connected]]~~.

	~~The Robertson graph is also a [[Hamiltonian graph]] which possesses {{formatnum:5376}} distinct directed Hamiltonian cycles.~~

	~~==Algebraic properties==~~
	~~The Robertson graph is not a [[vertex-transitive graph]]~~ and ~~its full automorphism group is isomorphic~~ to ~~the~~ [[dihedral group]] of order 24, the group of symmetries of a regular [[dodecagon]], including both rotations and reflections.<ref name="SURV">Geoffrey Exoo & Robert Jajcay, Dynamic cage survey, Electr. J. Combin. 15, 2008.</~~ref>~~

	~~The [[characteristic polynomial]~~] of the ~~Robertson graph is~~
	~~:<math>(x~~-~~4)(x-1)^2(x^2-3)^2(x^2+x-5)</math>~~
	:~~<math>(x^2+x-4)^2(x^2+x-3)^2(x^2+x-1)~~.\ <~~/math~~>

	~~==Gallery==~~
	<~~gallery~~>
	~~Image:Robertson graph~~.~~svg\|The Robertson graph as drawn in the original publication~~.
	~~Image:Robertson graph 3COL~~.~~svg\|The [[chromatic number]] of the Robertson graph~~ is~~ 3.~~
	~~Image:Robertson graph 5color edge~~.~~svg\|The [[chromatic index]]~~ of ~~the Robertson graph is 5~~.
	~~</gallery>~~

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

	~~[[Category:Individual graphs]]~~
	~~[[Category:Regular graphs]]~~

en>JmCor: Diacritics

2013-06-26T04:03:45Z

Diacritics

← Older revision		Revision as of 06:03, 26 June 2013
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			{{infobox graph
			\| name = Robertson graph
			\| image = [[Image:Robertson graph hamiltonian.svg\|240px]]
			\| image_caption = The Robertson graph is Hamiltonian.
			\| namesake = [[Neil Robertson (mathematician)\|Neil Robertson]]
			\| vertices = 19
			\| edges = 38
			\| automorphisms = 24 ([[dihedral group\|D<sub>12</sub>]])
			\| girth = 5
			\| diameter = 3
			\| radius = 3
			\| chromatic_number = 3
			\| chromatic_index = 5<ref>{{MathWorld\|urlname=Class2Graph\|title=Class 2 Graph}}</ref>
			\| properties = [[Cage (graph theory)\|Cage]]<br>[[Hamiltonian graph\|Hamiltonian]]
			}}
			In the [[mathematics\|mathematical]] field of [[graph theory]], the '''Robertson graph''' or '''(4,5)-cage,''' is a 4-[[regular graph\|regular]] [[undirected graph]] with 19 vertices and 38 edges named after [[Neil Robertson (mathematician)\|Neil Robertson]].<ref>{{MathWorld\|urlname=RobertsonGraph\|title=Robertson Graph}}</ref><ref>Bondy, J. A. and Murty, U. S. R. Graph Theory with Applications. New York: North Holland, p. 237, 1976.</ref>

			The Robertson graph is the unique [[cage graph\|(4,5)-cage graph]] and was discovered by Robertson in 1964.<ref>Robertson, N. "The Smallest Graph of Girth 5 and Valency 4." Bull. Amer. Math. Soc. 70, 824-825, 1964.</ref> As a cage graph, it is the smallest 4-regular graph with girth 5.

	~~Surely the second option would be more beneficial for any website. You may discover this probably the most time~~-~~consuming part of building a Word~~ - ~~Press MLM website~~. ~~These templates are professionally designed and are~~ also ~~Adsense ready~~. ~~If you are using videos on your site then this~~ is the ~~plugin to use. Also our developers are well convergent with~~ the ~~latest technologies and bitty-gritty~~ of ~~wordpress website design~~ and ~~promises to deliver you the best solution that you can ever have~~. <br>~~<br>Right starting from social media support to search engine optimization~~, ~~such plugins are easily available within the Word - Press open source platform. The higher your blog ranks on search engines~~, ~~the more likely people will find your online marketing site~~. ~~It allows Word - Press users to easily use HTML5 the element enable native video playback within the browser~~. ~~It primarily lays emphasis on improving the search engine results of your website whenever a related query is typed in the search box~~. ~~Many times the camera is following Mia~~, ~~taking in her point of view in almost every frame~~. <br><br>~~Should you have any inquiries regarding wherever in addition to the best way to employ [http://closegroup.org/moodle/user/view.php?id=852017&course=~~1 ~~wordpress backup plugin], you are able to e~~-~~mail us in our own web page. It is very easy to install Word~~ - Press blog or website. The only problem with most is that they only offer a monthly plan, you never own the software and you can’t even install the software on your site, you must go to another website to manage your list and edit your autoresponder. I hope this short Plugin Dynamo Review will assist you to differentiate whether Plugin Dynamo is Scam or a Genuine. To turn the Word - Press Plugin on, click Activate on the far right side of the list. There are plenty of tables that are attached to this particular database. <br><br>It is the convenient service through which professionals either improve the position or keep the ranking intact. I didn't straight consider near it solon than one distance, I got the Popup Ascendancy plugin and it's up and lengthways, likely you make seen it today when you visited our blog, and I yet customize it to fit our Thesis Wound which gives it a rattling uncomparable visage and search than any different popup you know seen before on any added journal, I hump arrogated asset of one of it's quatern themes to make our own. Thus it is difficult to outrank any one of these because of their different usages. The most important plugins you will need are All-in-One SEO Pack, some social bookmarking plugin, a Feedburner plugin and an RSS sign up button. It does take time to come up having a website that gives you the much needed results hence the web developer must be ready to help you along the route. <br><br>~~Millions of individuals and organizations are now successfully using this tool throughout the world~~. ~~When you sign up with Wordpress, you gain access to several different templates and plug-~~in ~~that allow you to customize your blog so that it fits in with your business website design seamlessly~~. ~~However, there are a few other Wordpress plugins also for its development which requires adding files in your Wordpress setup~~. ~~Working with a Word - Press blog and~~ the ~~appropriate cost-free Word - Press theme, you can get a professional internet site up and published in no time at all~~. ~~Article Source~~: ~~Hostgator discount coupons for your Wordpress site here~~.		It has [[chromatic number]] 3, [[chromatic index]] 5, diameter 3, radius 3 and is both 4-[[k-vertex-connected graph\|vertex-connected]] and 4-[[k-edge-connected graph\|edge-connected]].

			The Robertson graph is also a [[Hamiltonian graph]] which possesses {{formatnum:5376}} distinct directed Hamiltonian cycles.

			==Algebraic properties==
			The Robertson graph is not a [[vertex-transitive graph]] and its full automorphism group is isomorphic to the [[dihedral group]] of order 24, the group of symmetries of a regular [[dodecagon]], including both rotations and reflections.<ref name="SURV">Geoffrey Exoo & Robert Jajcay, Dynamic cage survey, Electr. J. Combin. 15, 2008.</ref>

			The [[characteristic polynomial]] of the Robertson graph is
			:<math>(x-4)(x-1)^2(x^2-3)^2(x^2+x-5)</math>
			:<math>(x^2+x-4)^2(x^2+x-3)^2(x^2+x-1).\ </math>

			==Gallery==
			<gallery>
			Image:Robertson graph.svg\|The Robertson graph as drawn in the original publication.
			Image:Robertson graph 3COL.svg\|The [[chromatic number]] of the Robertson graph is 3.
			Image:Robertson graph 5color edge.svg\|The [[chromatic index]] of the Robertson graph is 5.
			</gallery>

			== References ==
			{{reflist}}

			[[Category:Individual graphs]]
			[[Category:Regular graphs]]

en>DrMicro: /* Relationship to polynomials */

2012-02-27T13:32:21Z

Relationship to polynomials

New page

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