Half domination arrangements in regular and semi-regular tessellation   type graphs
  We study the problem of half-domination sets of vertices in vertex transitive infinite graphs generated by regular or semi-regular tessellations of the plane. In some cases, the results obtained are sharp and in the rest, we show upper bounds for the average densities of vertices in half-domination sets. 
Eugen J. Ionascu
math.CO math.OC