Inequalities of Nordhaus – Gaddum Type for Connected Domination

  title={Inequalities of Nordhaus – Gaddum Type for Connected Domination},
  author={Hosein Karami and Seyed Mahmoud Sheikholeslami},
A set S of vertices of a graph G is a connected dominating set if every vertex not in S is adjacent to some vertex in S and the subgraph induced by S is connected. The connected domination number γc(G) is the minimum size of a connected dominating set of G. In this paper we prove that γc(G) + γc(G) ≤ min{δ(G), δ(G)} + 4 for every n-vertex graph G such that G and G have diameter 2 and show that the bound is sharp for each value of the right side. Also, γc(G) + γc(G) ≤ 3n 4 if G and G are… CONTINUE READING