On minimum weakly connected independent sets for wireless sensor networks: properties and enumeration algorithm

@article{Bendali2015OnMW,
  title={On minimum weakly connected independent sets for wireless sensor networks: properties and enumeration algorithm},
  author={Fatiha Bendali and Jean Mailfert and Djelloul Mameri},
  journal={RAIRO Oper. Res.},
  year={2015},
  volume={49},
  pages={313-334}
}
Modeling topologies in Wireless Sensor Networks principally uses domination theory in graphs. Indeed, many dominating structures have been proposed as virtual backbones for wireless networks. In this paper, we study a dominating set that we call Weakly Connected Independent Set (wcis ). Given an undirected connected graph G = (V,E ), we say that an independent set S in G is weakly connected if the spanning subgraph (V, [ S,V \ S ]) is connected, where [ S,V \ S ] is the set of edges having… 
2 Citations
The weakly connected independent set polytope in corona and join of graphs
TLDR
A theorem about complete description of the wcis polytope has been given for 1-sum operation and a class of graphs is also inductively defined from the connected bipartite graphs, the cycles and the strongly chordal graphs, for which the MWWCISP is polynomially solvable.

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