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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] |
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Here's a nice little algorithm for constructing a self-complementary graph from a self-complementary graph $H$ with $4k$ or $4k+1$ vertices, $k = 1, 2, ...$ (e.g., from a self-complementary graph with $4$ vertices, one can construct a self-complementary graph with $8$ vertices; from $5$ vertices, construct one with $9$ vertices). See this PDF on constructing self-complementary graphs. |
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Systematically is easy; systematically and efficiently, I don't know. It's easy to work out how many edges such a graph must have, that's a start. There's also some information at http://oeis.org/A000171 |
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