On the (h,k)(h,k)-domination numbers of iterated line digraphs

An (h,k)(h,k)-dominating set in a digraph GG is a subset DD of V(G)V(G) such that the subdigraph induced by DD is hh-connected and for every vertex vv of GG, vv is in-dominated and out-dominated by at least kk vertices in DD. The (h,k)(h,k)-domination number γh,k(G)γh,k(G) of GG is the minimum cardinality of an (h,k)(h,k)-dominating set in GG. An (h,k)(h,k)-dominating set finds applications to fault-tolerant location problems of resources in communication networks and fault-tolerant virtual backbone in wireless networks.Let GG be a connected dd-regular digraph and 1≤k