I need your help for a couple of graph connectivity proofs!

**First one:**

For every simple graph G with

__prove that k(G)=d(G)__,where d(G) is the minimum vertex degree of the graph,

k(G) is the vertex connectivity and |V(G)| is the number of vertices.

**Second one:**

For every simple graph G with

__prove that G is a k-vertex-connected graph__, where d(G) is the minimum vertex degree of the graph.

Thank you!!