number of vertices in a self-complemntary graph Problem: Prove that the number of vertices of a self-complementary graph must be congruent to 0 or 1 modulo 4.
I think my starting point would be that P4 and C5 are self-complementary and proceed by induction by adding P4s.
I established the first step in a previous problem, but I need help on the induction step.
i.e. proving that adjoining P4 will indeed yield a self-complementary graph.

Hint: If a graph with $n$ vertices is self-complementary, then the complete graph on $n$ vertices has an even number of edges.
Hence $n \equiv 0, 1 \pmod{4} $.
