2021-045

Let $\overline{G}$ denote the complement graph of an undirected, loppless graph $G=(V,E)$, that is, $\overline{G}$ has the same set of vertices $V$, but the set of edges in $\overline{G}$ consists of every pair of vertices from $V$ that is not included in $E$.

How can we express the number of edges in $\overline{G}$ in terms of the sizes $v=|V|$ and $e=|E|$ ?

1. $$\frac{2v^2+2v+e}{2}$$
2. $$\frac{v^2-v-2e}{2}$$
3. $$\frac{2v^2-v+2e}{2}$$
4. $$\frac{v^2+2v-e}{2}$$
5. None of the above

Original idea by: Jader Martins