1) How many nodes does a ball of radius $r$ in the Johnson graph $J(n,k)$ contain (Volume)?
2) How many nodes $v$ does a ball with center $x$ of radius $r$ in the Johnson graph $J(n,k)$ contain such that $d(x,v)=r$ (Surface)?
The Jonhson Graph is defined here:
https://en.wikipedia.org/wiki/Johnson_graph
Any reference to this question would be very nice.