Séminaire Lotharingien de Combinatoire, B55c (2006), 13 pp.
S. Pirzada and U. Samee
Mark Sequences in Digraphs
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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