Geodesic
On imbalances in digraphs
Kragujevac Journal of Mathematics, Tome 31 (2008), p. 143

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The imbalance of a vertex in a digraph is defined as $b_{v_{i}}(\mbox{or simply\ } b_{i}) =d_{v_{i}}^{+}-d_{v_{i}}^{-}$, where $d_{v_{i}}^{+}$ and $d_{v_{i}}^{-}$ are respectively the outdegree and indegree of $v_i$. The set of imbalances of the vertices in a digraph is called its imbalance set. In this paper, we obtain an inequality for imbalances in simple directed graphs. Also, we give the existence of an oriented graph with a given imbalance set.
Classification : 05C20
Keywords: digraph, imbalance, outdegree, indegree, oriented graph, arc. 
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     author = {Shariefuddin Pirzada},
     title = {On imbalances in digraphs},
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Shariefuddin Pirzada. On imbalances in digraphs. Kragujevac Journal of Mathematics, Tome 31 (2008), p. 143 . http://geodesic.mathdoc.fr/item/KJM_2008_31_a11/