The following section provides information concerning the Rook Complement Graph family.

Definition:

The m×n rook complement graph is the graph complement of the m×n rook graph.

Value of Adjacency Matrix Game:

(m-1)(n-1)/mn

Value of M'' :

(n2m-n2-3mn+3n+2m-2)/(mn+1)(n-2)-n+3

Consider removing a vertex option from the column player, how will that then affect the game value?

The color green represents a decrease in the game value if the vertex is chosen, red represents an increase in the game value if the vertex is chosen, and blue represents no change in the game value.