Просмотр кода страницы (k,g)-Cage

'''<math>\,(k,g)</math>-Cage''' — ''[[(k,g)-Клетка|<math>\,(k,g)</math>-клетка]].'' 

For a given ordered pair of integers <math>\,(k,g)</math>, with <math>k \geq 2</math> and <math>g
\geq 3</math>, a <math>\,k</math>-[[regular graph]] with the smallest [[cycle]] length, or girth,
equal to <math>\,g</math> is said to be a <math>\,(k,g)</math>-graph. A '''<math>\,(k,g)</math>-cage''' is a
<math>\,(k,g)</math>-graph having the least number, <math>\,f(k,g)</math>, of [[vertex|vertices]]. We call
<math>\,f(k,g)</math> the '''[[cage number]]''' of a <math>\,(k,g)</math>-graph. One readily
observes that <math>\,(2,g)</math>-cages are cycles of length <math>\,g</math>, and
<math>\,(k,3)</math>-cages are [[complete graph|complete graphs]] of order <math>\,k+1</math>.

The unique <math>\,(3,7)</math>-cage known as the '''[[McGee graph]]''' is an example of
a cage that is not transitive. It has <math>\,24</math> vertices and its automorphism group has order <math>\,32</math>.

==Литература==

* Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.