Imbalances in directed multigraphs

Abstract

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.

References in corpus (1)

• Reconstruction of complete interval tournaments. II