Thread: connectivity 3 regular graph

if a graph G is 3 regular prove that vertex connectivity=edge connectivity

From any edge cut set you can build a corresponding vertex cut set with as many or fewer vertices, so vertex connectivity is never larger than edge connectivity. And if you build the other way round you'll only need more edges than vertices if any vertex (in your original cut set) is connected by two edges into each block. (Making it at least degree 4.)