Geodesic
On imbalances in digraphs
Kragujevac Journal of Mathematics, Tome 31 (2008), p. 143 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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},
     journal = {Kragujevac Journal of Mathematics},
     pages = {143 },
     year = {2008},
     volume = {31},
     zbl = {1199.05156},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2008_31_a11/}
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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/