# 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…

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## 2 Citations

The weakly connected independent set polytope in corona and join of graphs

- MathematicsJ. Comb. Optim.
- 2018

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.

The minimum weakly connected independent set problem: Polyhedral results and Branch-and-Cut

- MathematicsDiscret. Optim.
- 2016

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