Monsalve, Juan; Rada, Juan On the maximal energy among orientations of a tree. (English) Zbl 1474.05163 Kuwait J. Sci. 47, No. 3, 2-13 (2020). Summary: 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. This raises the question in general: Which orientations of a tree have maximal trace norm? Cited in 2 Documents MSC: 05C20 Directed graphs (digraphs), tournaments 05C35 Extremal problems in graph theory 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) 05C05 Trees Keywords:extremal values; digraph; orientation of a tree; trace norm PDFBibTeX XMLCite \textit{J. Monsalve} and \textit{J. Rada}, Kuwait J. Sci. 47, No. 3, 2--13 (2020; Zbl 1474.05163) Full Text: Link