Inequalities of NordhausGaddum type for doubly connected domination number
A set S S of vertices of a connected graph G G is a doubly connected dominating set  if every vertex not in S S is adjacent to some vertex in S S and the subgraphs induced by S S and V?S V ? S are connected. The doubly connected domination number ?cc(G) ? c c ( G ) is the minimum size of such a set. We prove that when G G and G  are both connected of order n n , ? c c ( G ) + ? c c ( G  ) ? n + 3 and we describe the two infinite families of extremal graphs achieving the bound.
doubly connected domination number doubly connected dominating set nordhausgaddum inequalities