Congestion game: Difference between revisions
Jump to navigation
Jump to search
en>KarlFrei m →Existence of Nash equilibria: I think not!! |
en>O.friedler No edit summary |
||
| Line 1: | Line 1: | ||
{{Infobox graph | |||
| name = Gewirtz graph | |||
| image = [[Image:Gewirtz graph embeddings.svg|300px]] | |||
| image_caption = Some embeddings with 7-fold symmetry. No 8-fold or 14-fold symmetry are possible. | |||
| vertices = 56 | |||
| edges = 280 | |||
| automorphisms = {{formatnum:80640}} | |||
| radius = 2 | |||
| diameter = 2 | |||
| girth = 4 | |||
| chromatic_number = 4 | |||
| properties = [[Strongly regular graph|Strongly regular]]<br>[[Hamiltonian graph|Hamiltonian]]<br>[[Triangle-free graph|Triangle-free]]<br>[[Vertex-transitive graph|Vertex-transitive]]<br>[[edge-transitive graph|Edge-transitive]]<br>[[distance-transitive graph|Distance-transitive]]. | |||
}} | |||
The '''Gewirtz graph''' is a [[strongly regular graph]] with 56 vertices and valency 10. It is named after the mathematician Allan Gewirtz, who described the graph in his dissertation.<ref>[http://genealogy.math.ndsu.nodak.edu/id.php?id=35587 Allan Gewirtz], ''Graphs with Maximal Even Girth'', Ph.D. Dissertation in Mathematics, City University of New York, 1967.</ref> | |||
==Construction== | |||
The Gewirtz graph can be constructed as follows. Consider the unique ''S''(3, 6, 22) [[Steiner system]], with 22 elements and 77 blocks. Choose a random element, and let the vertices be the 56 blocks not containing it. Two blocks are adjacent when they are disjoint. | |||
With this construction, one can embed the Gewirtz graph in the [[Higman–Sims graph]]. | |||
==Properties== | |||
The [[characteristic polynomial]] of the Gewirtz graph is | |||
: <math>(x-10)(x-2)^{35}(x+4)^{20}. \, </math> | |||
Therefore it is an [[integral graph]]. The Gewirtz graph is also determined by its spectrum. | |||
The [[independence number]] is 16. | |||
==Notes== | |||
{{Reflist}} | |||
==References== | |||
* {{cite web |url=http://www.win.tue.nl/~aeb/graphs/Sims-Gewirtz.html |title=Sims-Gewirtz graph |author=Brouwer, Andries}} | |||
* {{MathWorld|title=Gewirtz graph|urlname=GewirtzGraph}} | |||
[[Category:Individual graphs]] | |||
[[Category:Regular graphs]] | |||
[[Category:4-chromatic graphs]] | |||
Revision as of 18:51, 9 November 2013
The Gewirtz graph is a strongly regular graph with 56 vertices and valency 10. It is named after the mathematician Allan Gewirtz, who described the graph in his dissertation.[1]
Construction
The Gewirtz graph can be constructed as follows. Consider the unique S(3, 6, 22) Steiner system, with 22 elements and 77 blocks. Choose a random element, and let the vertices be the 56 blocks not containing it. Two blocks are adjacent when they are disjoint.
With this construction, one can embed the Gewirtz graph in the Higman–Sims graph.
Properties
The characteristic polynomial of the Gewirtz graph is
Therefore it is an integral graph. The Gewirtz graph is also determined by its spectrum.
The independence number is 16.
Notes
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.
References
- Template:Cite web
I had like 17 domains hosted on single account, and never had any special troubles. If you are not happy with the service you will get your money back with in 45 days, that's guaranteed. But the Search Engine utility inside the Hostgator account furnished an instant score for my launched website. Fantastico is unable to install WordPress in a directory which already have any file i.e to install WordPress using Fantastico the destination directory must be empty and it should not have any previous installation files. When you share great information, others will take note. Once your hosting is purchased, you will need to setup your domain name to point to your hosting. Money Back: All accounts of Hostgator come with a 45 day money back guarantee. If you have any queries relating to where by and how to use Hostgator Discount Coupon, you can make contact with us at our site. If you are starting up a website or don't have too much website traffic coming your way, a shared plan is more than enough. Condition you want to take advantage of the worldwide web you prerequisite a HostGator web page, -1 of the most trusted and unfailing web suppliers on the world wide web today. Since, single server is shared by 700 to 800 websites, you cannot expect much speed.
Hostgator tutorials on how to install Wordpress need not be complicated, especially when you will be dealing with a web hosting service that is friendly for novice webmasters and a blogging platform that is as intuitive as riding a bike. After that you can get Hostgator to host your domain and use the wordpress to do the blogging. Once you start site flipping, trust me you will not be able to stop. I cut my webmaster teeth on Control Panel many years ago, but since had left for other hosting companies with more commercial (cough, cough) interfaces. If you don't like it, you can chalk it up to experience and go on. First, find a good starter template design. When I signed up, I did a search for current "HostGator codes" on the web, which enabled me to receive a one-word entry for a discount. Your posts, comments, and pictures will all be imported into your new WordPress blog.
- ↑ Allan Gewirtz, Graphs with Maximal Even Girth, Ph.D. Dissertation in Mathematics, City University of New York, 1967.