6.4.22 Graph theory

Problem: Let \( G k \)-vertex connected. We form a new graph \( G^{\prime} \) from \( \mathrm{G} \) by adding a new vertex \( y \) to \( \mathrm{G} \) and at least \( k \) edges from \( y \) in \( k \) different vertices of the graph \( G \). Prove that \( G^{\prime} \) is also \( k \)-connected.