(k,g)-Cage: различия между версиями

'''<math>(k,g)</math>-Cage''' --- <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 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 graphs of order <math>k+1</math>.

The unique (3,7)-cage known as the '''McGee graph''' is an example of

a cage that is not transitive. It has 24 vertices and its automorphism

group has order 32.