The super-connectivity of Johnson graphs

Abstract

For positive integers $n,k$ and $t$, the uniform subset graph $G(n,k,t)$ has all $k$-subsets of $\{1,2,\dots ,n\}$ 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 $n\ge k\ge 1$.

References in corpus (2)

• Graph Isomorphism in Quasipolynomial Time
• The girth, odd girth, distance function, and diameter of generalized Johnson graphs