Geodesic
Mark Sequences in Digraphs
Séminaire lotharingien de combinatoire, Tome 55 (2005-2007) 
S. Pirzada; U. Samee. Mark Sequences in Digraphs. Séminaire lotharingien de combinatoire, Tome 55 (2005-2007). http://geodesic.mathdoc.fr/item/SLC_2005-2007_55_a2/
@article{SLC_2005-2007_55_a2,
     author = {S. Pirzada and U. Samee},
     title = {Mark {Sequences} in {Digraphs}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2005-2007},
     volume = {55},
     url = {http://geodesic.mathdoc.fr/item/SLC_2005-2007_55_a2/}
}
TY  - JOUR
AU  - S. Pirzada
AU  - U. Samee
TI  - Mark Sequences in Digraphs
JO  - Séminaire lotharingien de combinatoire
PY  - 2005-2007
VL  - 55
UR  - http://geodesic.mathdoc.fr/item/SLC_2005-2007_55_a2/
ID  - SLC_2005-2007_55_a2
ER  - 
%0 Journal Article
%A S. Pirzada
%A U. Samee
%T Mark Sequences in Digraphs
%J Séminaire lotharingien de combinatoire
%D 2005-2007
%V 55
%U http://geodesic.mathdoc.fr/item/SLC_2005-2007_55_a2/
%F SLC_2005-2007_55_a2

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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.