Efficient routing among mobile hosts is an important function in ad hoc networks. Routing based on a connected dominating set is a promising approach, where the search space for a route is reduced to the hosts in the set. A set is dominating if all the hosts are either in the set or neighbors of hosts in the set. The efficiency of dominating-set-based routing mainly depends on the overhead intr...

A dominating set D of a graph G is a subset of V (G) such that for every vertex v ∈ V (G), either v ∈ D or there exists a vertex u ∈ D that is adjacent to v in G. Dominating sets of small cardinality are of interest. A connected dominating set C of a graph G is a dominating set of G such that the subgraph induced by the vertices of C in G is connected. A weakly-connected dominating set W of a g...

A dominating set S of a graph is a metric-locating-dominating set if each vertex of the graph is uniquely distinguished by its distances from the elements of S, and the minimum cardinality of such a set is called the metric-locationdomination number. In this paper, we undertake a study that, in general graphs and specific families, relates metric-locating-dominating sets to other special sets: ...

We prove that the problem of nding two minimum dominating sets (connected dominating sets or vertex clique covers) with minimum intersection is linearly solvable in interval graphs. Furthermore, the problem of deciding whether or not there exist two disjoint minimum dominating sets (connected dominating sets or vertex clique covers) is shown to be NP-hard for chordal graphs.