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
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.
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!