As a generalization of connected domination in a graph G we consider domination by sets having at most k components. The order γ c (G) of such a smallest set we relate to γc(G), the order of a smallest connected dominating set. For a tree T we give bounds on γ c (T ) in terms of minimum valency and diameter. For trees the inequality γ c (T ) ≤ n− k − 1 is known to hold, we determine the class o...

—In this paper, a Connected Dominating Set (CDS) construction algorithm CSCDS (Connected Subset based CDS) is proposed, which is based on the connected subset concept. The CSCDS contains two main stages, which are dominating set construction stage and connected dominating set construction stage respectively. In the first stage, the dominators are proposed based on the one hop white neighbor in...

A connected dominating set of a graph G = (V, E) is a subset of vertices CD ⊆ V such that every vertex not in CD is adjacent to at least one vertex in CD, and the subgraph induced by CD is connected. We show that, given an arc family F with endpoints sorted, a minimum-cardinality connected dominating set of the circular-arc graph constructed from F can be computed in O(|F |) time.

Article history: Received 14 November 2008 Received in revised form 15 January 2012 Accepted 27 February 2012 Available online xxxx

Many authors studied cooperative games that arise from variants of dominating set games on graphs. In wireless networks, the connected dominating set is used to reduce routing table size and communication cost. In this paper, we introduce a connected dominating set game to model the cost allocation problem arising from a connected dominating set on a given graph and study its core. In addition,...