Given a graph, is there any algorithm to build from it a self-complementary graph, by adding edges and vertices? I'm also interested in minimizing the number of added nodes.
Thank you!
2026-03-30 20:47:26.1774903646
Construct self-complementary graph
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Say you have a graph $G$, with complement $G^c$. Create a new graph: $$G \equiv G^c \equiv G^c \equiv G$$ where $H_1 \equiv H_2$ means that every vertex in $H_1$ is connected to every vertex in $H_2$. Then this graph is self complementary (why?) and since it contains a copy of $G$, it can be built up from $G$.