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Séminaire Lotharingien de Combinatoire, B55c (2006), 13 pp.

# S. Pirzada and U. Samee

# Mark Sequences in Digraphs

**Abstract.**
A *k*-digraph is an orientation of a multi-graph that is
without loops and contains at most *k* edges between any pair of distinct
vertices. We obtain necessary and sufficient conditions for a sequence of
non-negative integers in non-decreasing order to be a sequence of numbers,
called marks (*k*-scores), attached to vertices of a *k*-digraph. We characterize
irreducible mark sequences in *k*-digraphs and uniquely realizable mark
sequences in 2-digraphs.

Received: September 21, 2005.
Revised: June 1, 2006.
Accepted: July 3, 2006.

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