Is there any code to list all minimal k-distance dominating sets of a simple graph G in sagemath?

savecancel

You can use method minimal_dominating_sets to list the minimal distance-2 dominating sets on a modified graph H. The modified graph H has an edge between u and v if these vertices are at distance at most 2 in G.

sage: G = graphs.PathGraph(5)
sage: H = G.copy()
sage: for u in G:
....:     H.add_edges((u, v) for v in G.breadth_first_search(u, distance=2) if u != v)
sage: for d in H.minimal_dominating_sets():
....:     print(d)
{0, 3}
{1, 3}
{2}
{0, 4}
{1, 4}