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On the behaviour of sequences of iterated eccentric digraphs

The eccentric digraph ED(G) of a digraph G has the same vertex set as G, but with an arc from u to v in ED(G) iff v is an eccentric vertex of u in G. Given a positive integer k, the kth iterated eccentric digraph of G is defined as EDk(G) = ED(EDk−1(G)). We study the period and tail of the sequence {ED(G)}k when G is a labelled [unlabelled] digraph.