On imbalances in digraphs

Shariefuddin Pirzada

Kragujevac Journal of Mathematics, Tome 31 (2008) no. 1.

Résumé

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.