Constructing self-complementary graphs How does one go about systematically constructing a self-complementary graph, on say 8 vertices?
[Added: Maybe everyone else knows this already, but I had to look up my guess to be sure it was correct: a self-complementary graph is a simple graph which is isomorphic to its complement.  --PLC]

If every prime factor of $n$ is $1\bmod 4$ then there is an easy circulant graph that is self complementary.
What you do is let the vertices be the congruence classes from $0$ to $n-1 \bmod n$ and then you add an edge between two vertices if their difference is a quadratic residue $\bmod p$ for an even number of primes $p$ dividing $n$. (you need $p$ to be $1\bmod 4$ so that it doesn't matter if you take the positive or negative difference).
To see the graph is self complementary you notice that multiplying every vertex by a residue that is a primitive root $\bmod p^k$ for all $p$ is an isomorfism into the complement graph ( or any number that is a non-quadratic residue $\bmod$ every $p$).
