Imbalances in directed multigraphs

Details Imbalances in directed multigraphs Imbalances in directed multigraphs

2010-12-25

arxiv.org/abs/1012.5447v1

Acta Univ. Sapientiae, Mathematica, 2 (2010), 137--145

Mathematics

Combinatorics

Scientific paper

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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