Making a dominating set of a graph connected
Hengzhe Li, Baoyindureng Wu, Weihua Yang · Discussiones Mathematicae Graph Theory · 2018
Let G = (V, E) be a graph and S ⊆ V .We say that S is a dominating set of G, if each vertex in V \ S has a neighbor in S.Moreover, we say that S is a connected (respectively, 2-edge connected or 2-connected) dominating set of G if G[S] is connected (respectively, 2-edge connected or 2-connected).The domination (respectively, connected domination, or 2edge connected domination, or 2-connected domination) number of G is the cardinality of a minimum dominating (respectively, connected dominating, or 2-edge connected dominating, or 2-connected dominating) set of G, and is