74.69.73.189: /* Definition */ Fixed "such POLYNOMIALS are 'polynomial functors' " to "such FUNCTORS are 'polynomial functors' ". Also changed "THE simplifying condition" to "A simplifying condition".

2013-11-05T07:47:31Z

Definition: Fixed "such POLYNOMIALS are 'polynomial functors' " to "such FUNCTORS are 'polynomial functors' ". Also changed "THE simplifying condition" to "A simplifying condition".

← Older revision		Revision as of 09:47, 5 November 2013
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			\| name = Balaban 10-cage
			\| image = [[Image:Balaban 10-cage.svg\|220px]]
			\| image_caption = The Balaban 10-cage
			\| namesake = A. T. Balaban
			\| vertices = 70
			\| edges = 105
			\| automorphisms = 80
			\| girth = 10
			\| diameter = 6
			\| chromatic_number = 2
			\| chromatic_index = 3
			\| properties = [[Cubic graph\|Cubic]]<br>[[Cage (graph theory)\|Cage]]<br>[[Hamiltonian graph\|Hamiltonian]]
			}}
			In the [[mathematics\|mathematical]] field of [[graph theory]], the '''Balaban 10-cage''' or '''Balaban (3-10)-cage''' is a 3-[[regular graph]] with 70 vertices and 105 edges named after [[Alexandru Balaban\|A. T. Balaban]].<ref>{{MathWorld\|urlname=Balaban10-Cage\|title=Balaban 10-Cage}}</ref> Published in 1972,<ref>A. T. Balaban, A trivalent graph of girth ten, J. Combin. Theory Ser. B 12, 1-5. 1972.</ref> It was the first (3-10)-[[cage graph\|cage]] discovered but is not unique.<ref>Pisanski, T.; Boben, M.; Marušič, D.; and Orbanić, A. "The Generalized Balaban Configurations." Preprint. 2001. [http://citeseer.ist.psu.edu/448980.html].</ref>

			The complete list of (3-10)-cage and the proof of minimality was given by O'Keefe and Wong.<ref>M. O'Keefe and P.K. Wong, A smallest graph of girth 10 and valency 3, J. Combin. Theory Ser. B 29 (1980) 91-105.</ref> There exists 3 distinct (3-10)-cages, the other two being the [[Harries graph]] and the [[Harries-Wong graph]].<ref>Bondy, J. A. and Murty, U. S. R. Graph Theory with Applications. New York: North Holland, p. 237, 1976.</ref> Moreover, the Harries-Wong graph and Harries graph are [[Spectral graph theory\|cospectral graphs]].

			The Balaban 10-cage has chromatic number 2, chromatic index 3, diameter 6, girth 10 and is hamiltonian. It is also a 3-[[k-vertex-connected graph\|vertex-connected graph]] and a 3-[[k-edge-connected graph\|edge-connected graph]].

			The [[characteristic polynomial]] of the Balaban 10-cage is : <math>(x-3) (x-2) (x-1)^8 x^2 (x+1)^8 (x+2) (x+3) (x^2-6)^2 (x^2-5)^4 (x^2-2)^2 (x^4-6 x^2+3)^8</math>.

			==Gallery==
			<gallery>
			Image:balaban_10-cage_2COL.svg\|The [[chromatic number]] of the Balaban 10-cage is 2.
			Image:balaban_10-cage_3color_edge.svg\|The [[chromatic index]] of the Balaban 10-cage is 3.
			Image: balaban_10-cage_alternative_drawing.svg\|Alternative drawing of the Balaban 10-cage.
			</gallery>
			==See also==
			[[Molecular graph]]

			== References ==
			{{reflist}}

			{{DEFAULTSORT:Balaban 10-Cage}}
			[[Category:Individual graphs]]
			[[Category:Regular graphs]]

en>Ocsenave: rewrite for clarity

2011-12-22T08:45:50Z

rewrite for clarity

New page

Surely the second option would be more beneficial for any website. It is very easy to customize plugins according to the needs of a particular business. I thought about what would happen by placing a text widget in the sidebar beneath my banner ad, and so it went. If you are using videos on your site then this is the plugin to use. All this is very simple, and the best thing is that it is totally free, and you don't need a domain name or web hosting. You just download ready made templates to a separate directory and then choose a favorite one in the admin panel. When you write a new post, you'll see a small bar that goes across the text input area. Several claim that Wordpress just isn't an preferred tool to utilise when developing a professional site. They provide many such popular products which you can buy for your baby. Now a days it has since evolved into a fully capable CMS platform which make it, the best platform in the world for performing online business. Here are a few reasons as to why people prefer Word - Press over other software's. The following piece of content is meant to make your choice easier and reassure you that the decision to go ahead with this conversion is requited with rich benefits:. Whether or not it's an viewers on your web page, your social media pages, or your web page, those who have a present and effective viewers of "fans" are best best for provide provides, reductions, and deals to help re-invigorate their viewers and add to their main point here. Storing write-ups in advance would have to be neccessary with the auto blogs. Article Source: Stevens works in Internet and Network Marketing. There has been a huge increase in the number of developers releasing free premium Word - Press themes over the years. Cameras with a pentaprism (as in comparison to pentamirror) ensure that little mild is lost before it strikes your eye, however these often increase the cost of the digital camera considerably. However, you may not be able to find a theme that is in sync with your business. Fast Content Update - It's easy to edit or add posts with free Wordpress websites. Fortunately, Word - Press Customization Service is available these days, right from custom theme design, to plugin customization and modifying your website, you can take any bespoke service for your Word - Press development project. Should you beloved this informative article along with you would like to get details with regards to [http://shortener.us/backup_plugin_1496913 wordpress backup plugin] i implore you to check out the internet site. He loves sharing information regarding wordpress, Majento, Drupal and Joomla development tips & tricks. Visit our website to learn more about how you can benefit. In simple words, this step can be interpreted as the planning phase of entire PSD to wordpress conversion process. It is a fact that Smartphone using online customers do not waste much of their time in struggling with drop down menus. Likewise, professional publishers with a multi author and editor setup often find that Word - Press lack basic user and role management capabilities.

Calculus of functors - Revision history

74.69.73.189: /* Definition */ Fixed "such POLYNOMIALS are 'polynomial functors' " to "such FUNCTORS are 'polynomial functors' ". Also changed "THE simplifying condition" to "A simplifying condition".

en>Ocsenave: rewrite for clarity