Foolproof eternal domination in the all-guards move model
The eternal domination problem requires a graph be protected against an infinitely long sequence of attacks at vertices, by guards located at vertices, with the requirement that the configuration of guards induces a dominating set at all times. An attack is defended by sending a guard from a neighboring vertex to the attacked vertex. We allow all guards to move to neighboring vertices in response to an attack, but allow the attacked vertex to choose which neighboring guard moves to the attacked vertex. This is the all-guards move version of the "foolproof" eternal domination problem that has been previously studied. We present some results and conjectures on this problem. © 2012 Versita Warsaw and Springer-Verlag Wien.
Digital Object Identifier (DOI)
Klostermeyer, & MacGillivray, G. (2012). Foolproof eternal domination in the all-guards move model. Mathematica Slovaca, 62(4), 595–610. https://doi.org/10.2478/s12175-012-0033-x