On Minimal Geodetic Domination in Graphs
Let G be a connected graph. For two vertices u and v in G, a u-v geodesic is any shortest path joining u and v. The closed geodetic interval IG[u, v] consists of all vertices of G lying on any u-v geodesic. For S ⊆ V (G), S is a geodetic set in G if ∪u,v∈S IG[u, v] = V (G). Vertices u and v of G are neighbors if u and v are adjacent. The closed neighborhood NG[v] of vertex v consists of v and all neighbors of v. For S ⊆ V (G), S is a dominating set in G if ∪u∈S NG[u] = V (G). A geodetic dominating...