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### List of all dominating sets in a graph

The inbuilt function in sage for dominating set of a graph $G$ is

# G.dominating_set()

But this gives only a minimum dominating set of the graph. What I want is the list of all dominating sets of the graph. How to get this? Besides in the inbuilt function we have some additional options, like dominating_set(independent=True) which gives a minimum independent dominating set of the graph. Now if I want a minimum dominating set with some other properties, how to set it? For example if I need a minimal dominating set D so that in the graph there is no edge connecting two vertices of D.

### List of all dominating sets in a graph

The inbuilt function in sage for dominating set of a graph $G$ is

# G.dominating_set()

But this gives only a minimum dominating set of the graph. What I want is the list of all dominating sets of the graph. How to get this? Besides in the inbuilt function we have some additional options, like dominating_set(independent=True) which gives a minimum independent dominating set of the graph. Now if I want a minimum dominating set with some other properties, how to set it? For example if I need a minimal dominating set D so that in the graph there $D^c$(complement of D) is no edge connecting two vertices of D.independent.