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On the trace norms of orientations of graphs. (English) Zbl 1448.05129

Summary: The trace norm of the digraph is defined as the sum of the singular values of its adjacency matrix. We determine the orientations with, respectively, small and large trace norms among orientations of trees and unicyclic graphs, respectively.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C20 Directed graphs (digraphs), tournaments
15A18 Eigenvalues, singular values, and eigenvectors
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