  For positive integers $n,k$ and $t$, the uniform subset graph $G(n, k, t)$
has all $k$-subsets of $\{1,2,\ldots, n\}$ as vertices and two $k$-subsets are
joined by an edge if they intersect at exactly $t$ elements. The Johnson graph
$J(n,k)$ corresponds to $G(n,k,k-1)$, that is, two vertices of $J(n,k)$ are
adjacent if the intersection of the corresponding $k$-subsets has size $k-1$. A
super vertex-cut of a connected graph is a set of vertices whose removal
disconnects the graph without isolating a vertex and the super-connectivity is
the size of a minimum super vertex-cut. In this work, we fully determine the
super-connectivity of the family of Johnson graphs $J(n,k)$ for $n\geq k\geq
1$.
