Let $G$ be a simple undirected graph (no loops nor multi edges), $n=|v|$

My try:

Let $A,B,C,D$ be my vertices with no edges between them, their $deg.=0$ so the condition holds.

I can assign only $\large\lceil\frac{n}{2}\rceil$ distinct $degrees$ because every $v$ has an $even\space degree$.

But how to show that at least $3 \space vertices $ have same $degree ?$ (I can draw it by adding edge after edge to my nodes but it doesn't give me any new clues)