Order and Size of Graph do not determine Degrees of Vertices

Theorem
Let $G = \struct {V, E}$ be a simple graph.

Let both the order $\card V$ and size $\card E$ of $G$ be given.

Then it is not always possible to determine the degrees of each of the vertices of $G$.

Proof
The following $2$ simple graphs both have order $4$ and size $4$:


 * Chartrand-exercise-2-1-6.png

But:
 * the graph on the left has vertices with degrees $1, 2, 2, 3$
 * the graph on the right has vertices with degrees $2, 2, 2, 2$.