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Imbalances in directed multigraphs. (English)
Acta Univ. Sapientiae, Math. 2, No. 2, 137-145 (2010).
Summary: In a directed multigraph, the imbalance of a vertex $v_i$ is defined as $b_{v_i}= d^+_{v_i}- d^-_{v_i}$, where $d^+_{v_i}$ and $d^-_{v_i}$ denote the outdegree and indegree respectively of $v_i$. We characterize imbalances in directed multigraphs and obtain lower and upper bounds on imbalances in such digraphs. Also, we show the existence of a directed multigraph with a given imbalance set.
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