Proceedings of the 29th Canadian Conference on Computational Geometry, CCCG 2017, July 26-28, 2017, Carleton University, Ottawa, Ontario, Canada

The concept of power domination emerged from the problem of monitoring electrical systems. Given a graph G and a set S ⊆ V (G), a set M of monitored vertices is built as follows: at first, M contains only the vertices of S and their direct neighbors, and then each time a vertex in M has exactly one neighbor not in M , this neighbor is added to M . The power domination number of a graph G is the minimum size of a set S such that this process ends up with the set M containing every vertex of G. We here show that the power domination number of a triangular grid Tk with hexagonal-shape border of length k − 1 is exactly ⌈ k