Let's say $G$ is the graph for the legal moves of the rook in a chess board where the nodes corresponds to squares in the board; thus, there are 64 nodes present. I am trying to figure out #edges in $G$.
I think, there should be $ \binom{8}{2} $ edges for each column and $ \binom{8}{2} $ for each row. Since there are 8 rows and 8 columns in the chess board the solution is: $$ 8 * \binom{8}{2} + 8 * \binom{8}{2} $$
Is it correct? If not, why not?
Note: You can see the movements of the rook at http://en.wikipedia.org/wiki/Chess#Movement.