I was reading this solution and think there is a mistake in its proof. My doubt is how can $$\frac{v(v-1)}{2}+\frac{v(v-1)}{2}=\frac{v(v-1)}{4}$$? It should be a mistake?
Show that if G is a self-complementary simple graph with v vertices, then v ≡ 0 or 1 (mod 4)?
1
$\begingroup$
graph-theory
1 Answers
2
There is no mistake. We have that $|E(G)| = |E(\overline{G})|$ since $G \cong \overline{G}$ and $|E(G)| + |E(\overline{G})| = \frac{|G|(|G| - 1)}{2}$. Then $|E(G)| = \frac{|G|(|G| - 1)}{4}$.