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Maximal orientations of graphs. (English) Zbl 1444.05090

Summary: Orientations of connected graphs that maximize the spectral norm of the adjacency matrix are studied, and a conjecture of C. Hoppen et al. [Linear Algebra Appl. 574, 167–181 (2019; Zbl 1411.05163)] is solved.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C20 Directed graphs (digraphs), tournaments
05C40 Connectivity
05C85 Graph algorithms (graph-theoretic aspects)
15A18 Eigenvalues, singular values, and eigenvectors

Citations:

Zbl 1411.05163
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References:

[1] M. Behzad, G. Chartrand, and L. Lesniak-Foster.Graphs and Digraphs. Wadsworth, 1986. · Zbl 0403.05027
[2] C. Hoppen, J. Monsalve, and V. Trevisan.Linear Algebra and its Applications, 574:167-181, 2019.
[3] R.A. Horn and C.J. Johnson.Matrix Analysis(second edition). Cambridge University Press, Cambridge, 2012
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