I'm reading Richard J. Trudeau's book "Introduction to Graph Theory", in ch 2 there's an exercise:
Exercises 16. Find a self-complementary graph with $v=8$. Of the 12,346 graphs with $v=8$ only four are self-complementary.
The answer is given in page 199:
The names are those of students who found them.
However, I came out with something as:
- I paint $K_8$ edges as blue and red in Fig (a)
- then detach them in Fig (b)
- so both blue and red part are actually isomorphic to Fig (c)
Looks like I find a self-complementary graph of $v=8$.
The problem is, the one I found, is not isomorphic to any of the 4 graphs given in the answer: it has 4 vertices of degree 5, only the graph by Fanny Zambuto has this feature; but then Fanny's 4 triangles do not share edges while mine do.
So where did I miss?