# Find a self-complementary graph with $v = 8$. Of the $12, 346$ graphs with $v = 8$ only four are self-complementary.

This is Trudeau's exercise 2.16:

Find a self-complementary graph with $v = 8$. Of the $12, 346$ graphs with $v = 8$ only four are self-complementary.

The picture in below is the answer that the book itself provides: And the picture in below is the answer that I have found: Given that the book says there are only four graphs that are self-complementary with $v = 8$ did I discover two new ones or my graphs are somehow isomorphic to those provided by the book?

Note: My graphs are drawn with their complements in one figure hence the different colors.

If my graphs are isomorphic to those provided by the book, could you please provide the labels of vertices that make them isomorphic? Where is my mistake?

To complement Michal's answer, you can see that your left graph is Fanny Zambuto by keeping the edge relations you have, but by permuting the locations $A \mapsto C \mapsto E \mapsto G \mapsto A$.
• And we can see that the right graph isn't any of the four because its degree sequence $2,2,2,2,5,5,5,5$ doesn't match any of the examples except Fanny Zambuto, but (unlike Fanny) its degree-$2$ vertices come in pairs which have the same degree-$5$ neighbors. – Misha Lavrov Aug 22 '18 at 16:47