The use of mobile guards to protect a graph has received much attention in the literature of late in the form of eternal dominating sets, eternal vertex covers and other models of graph protection. In this paper, eternal independent sets are introduced. These are independent sets such that the following can be iterated forever: a vertex in the independent set can be replaced with a neighboring vertex and the resulting set is independent.
Caro, Yair and Klostermeyer, William F.
"Eternal Independent Sets in Graphs,"
Theory and Applications of Graphs: Vol. 3
, Article 3.
Available at: http://digitalcommons.georgiasouthern.edu/tag/vol3/iss1/3