Hi everyone!
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!!