# Show a simple, no loop, 3 connected graph for which $\min(\deg(v))> \text { edge connectivity } > \text {vertex- connectivity }$

QUESTION

Show a simple, no loop, 3 connected graph for which $\min(\deg(v))> \text { edge connectivity } > \text {vertex- connectivity}$.

Attempt

I tried going from a wheel (which are 3 connected) and adding some random vertices and edges all around but I couldn't get it to work. Then I started with some different complete graphs, which didn't help either.

Could you give me some tips on how to construct a graph of this type? More generally, what if the question asks for a $n$-connected graph?

with minimum degree $5$, edge connectivity $4$ and vertex connectivity $3$.