I want to draw a graph of 8 vertices and 16 edges with maximum vertex connectivity and maximum edge connectivity and also draw a graph with minimum vertex connectivity and minimum edge connectivity .but l have no idea, please help.(i means that i want to two different graph but both are 16 edges and 8 vertices)
$\endgroup$ 11 Answer
$\begingroup$The example with minimum connectivity is trivial, just take a disconnected graph with $8$ vertices and $16$ edges, to do this take a copy of $K_7$ and an isolated vertex, and remove any $3$ edges you want.
To get the example with maximum connectivity first notice that the average degree is $4$, so the maximum edge-connectivity is at most $3$, and consequently the maximum vertex connectivity is also at most $3$.
The following graph reaches these connectivities:
