Worst-case efficient dominating sets in digraphs

Let 1≤n∈Z. Worst-case efficient dominating sets in digraphs   are conceived so that their presence in certain strong digraphs ST→n corresponds to that of efficient dominating sets in star graphs STnSTn. The fact that the star graphs STnSTn form a so-called dense segmental neighborly EE-chain is reflected in a corresponding fact for the digraphs ST→n. Related chains of graphs and open problems are presented as well.