The minimal size of a graph with generalized connectivity ${\kappa }_3=2$

Shasha Li, Xueliang Li, Yongtang Shi

Let $G$ be a nontrivial connected graph of order $n$ and $k$ an integer with $2\le k\le n$. For a set $S$ of $k$ vertices of $G$, let $\kappa (S)$ denote the maximum number $\ell$ of e…