Perfect Dominating Sets

  title={Perfect Dominating Sets},
  author={Marilynn Livingston and Quentin F. Stout},
A dominating setS of a graphG is perfectif each vertex ofG is dominated by exactly one vertex in S. We study the existence and construction of PDSs in families of graphs arising from the interconnection networks of parallel computers. These include trees, dags, series-parallel graphs, meshes, tori, hypercubes, cube-connected cycles, cube-connected paths, and de Bruijn graphs. For trees, dags, and series-parallel graphs we give linear time algorithms that determine if a PDS exists, and generate… CONTINUE READING