K-vertex-connected graph

A **k-vertex-connected graph** (or simply a **k-connected graph**) is a type of graph in which there are at least \( k \) vertex-disjoint paths between any two vertices. In other words, a graph is k-vertex-connected if: 1. It has at least \( k \) vertices. 2. It remains connected even after the removal of any \( k-1 \) vertices.