Is there any efficient algorithm to find the total number of dominant sets for a given graph? For example, in the image shown, A graph with three vertices has the following dominant sets: { {A, C}, {B}, {B, C}, {A, B}, {A,B,C} } giving a total of 5 dominant sets.
For another example, in the image below, A graph with four vertices has the following dominant sets: { {A, B}, {A, C}, {A, D}, {B, C}, {B, D}, {C,D}, {A, B, C}, {A, B, D}, {A, C, D}, {B, C, D}, {A, B, C, D} } giving a total of 11 dominant sets. My question is to find this count (If there is any method to get count only without dominant sets is also fine).
