Degree sequence for k-arc strongly connected multiple digraphs

Let D be a digraph on {v(1), ... , v(n)}. Then the sequence {(d(+)(v(1)), d(-)(v(1))), ... , (d(+)(v(n)), d(-)(v(n)))} is called the degree sequence of D. For any given sequence of pairs of integers d = {( d(1)(+), d(1)(-)), ... , (d(n)(+), d(n)(-))}, if there exists a k-arc strongly connected digraph D such that d is the degree sequence of D, then d is realizable and D is a realization of d. In this paper, characterizations for k-arc-connected realizable sequences and realizable sequences with arc-connectivity exactly k are given.