On the maximal energy among orientations of a tree - Rada, Juan; Monsalve, Juan (Kuwait Journal of Science, 2020)
The trace norm of a digraph is the trace norm of its adjacency matrix, i.e. the sum of its singular values. Given a bipartite graph $G$, it is well known that the sink-source orientations have minimal trace norm among all orientations of $G$. In this paper we show that the balanced orientations of $G$ attain the maximal trace norm when $G$ is a tree with separated branching vertices or when $G$ is a double-star tree. We give examples of trees (with adjacent branching vertices) where non-balanced orientations have maximal trace norm and raise the question in general: which orientations of a tree have maximal trace norm?