A total dominating set of a graph G = (V,E) is a subset D ⊆ V such that every vertex in V is adjacent to some vertex in D. Finding a total dominating set of minimum size is NPcomplete on planar graphs and W [2]-complete on general graphs when parameterized by the solution size. By the meta-theorem of Bodlaender et al. [FOCS 2009], it follows that there exists a linear kernel for Total Dominatin...

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...

One of the critical issues in wireless sensor network is the design of a proper routing protocol. One possible approach is utilizing a virtual infrastructure, which is a subset of sensors to connect all the sensors in the network. Among the many virtual infrastructures, the connected dominating set is widely used. Since a small connected dominating set can help to decrease the protocol overhead...

A mobile ad-hoc network (MANET), a set of wirelessly connected sensor nodes, is a dynamic system that executes hop-by-hop routing independently with no external help of any infrastructure. Proper selection of cluster heads can increase the life time of the Ad-hoc network by decreasing the energy consumption. Although different methods have been successfully proposed by researchers to tackle...

A set of vertices in a graph is perfect dominating if every vertex outside the set is adjacent to exactly one vertex in the set, and is neighborhood connected if the subgraph induced by its open neighborhood is connected. In any graph the full set of vertices is perfect dominating, and in every connected graph the full set of vertices is neighborhood connected. It is shown that (i) in a connect...

With a small battery equiped in each sensor, a large number of sensor are deployed in a specified area for many different application. Each sensor will perform two simple tasks of collecting (sensing) the surrounding inviroment and delivering the information to the central. While the equiped battery is irreplaceable, many researches concentrate on the extending the networks formed by these sens...