# Find a graph that has a high minimum degree, but low connectivity and edge connectivity

I've been stuck on this for a while. First, some definitions, in case my prof uses different terms than everyone else.

Minimum degree: This is equal to the number of edges connected to the vertex that has the least number of edges incident to it.

Connectivity: The larges number k, such that the graph is k-connected.

k-connected: A graph G is k-connected if there doesn't exist any set of vertices, call it X, such that the size of X is less than k, and G - X is disconnected.

Edge Connectivity: The larges value l, such that that there doesn't exist a set of edges, call it F, such that the size of F is less than l, and G - F is disconnected

So the question asks us to find a graph that has a high minimum degree but low connectivity and edge connectivity. I think I've made one with high minimum degree and low connectivity

The above is 1-connected but has minimum degree of 4.

However, I can't figure out a graph that has high minimum degree but low edge connectivity. Would appreciate some help.

Thanks.

I made this graph on https://illuminations.nctm.org/Activity.aspx?id=3550 EDIT: I made a mistake. The four corner vertices had degrees of 2. This following graph is the graph I was looking for:

It has a minimum degree of four. A connectivity of 1 and edge connectivity of 1. Thanks for the help!

Would separating $A$ into two nodes connected by one edge work? Also, the minimum degree of your graph is $2$ at each of the four corner nodes.