  There has been recent growing interest in graph theoretical properties known
as r- and (r,s)-robustness. These properties serve as sufficient conditions
guaranteeing the success of certain consensus algorithms in networks with
misbehaving agents present. Due to the complexity of determining the robustness
for an arbitrary graph, several methods have previously been proposed for
identifying the robustness of specific classes of graphs or constructing graphs
with specified robustness levels. The majority of such approaches have focused
on undirected graphs. In this paper we identify a class of scalable directed
graphs whose edge set is determined by a parameter k and prove that the
robustness of these graphs is also determined by k. We support our results
through computer simulations.
