Acyclic Digraphs and Eigenvalues of O,1 Matrices
By Brendan D. McKay, Frédérique E. Oggier, G. Royle, N. J. A. Sloane, Ian M. Wanless, H. Wilf. 2003
53 citations recorded by the source corpus.
We show that the number of acyclic directed graphs with n labeled vertices is equal to the number of n X n (0,1)-matrices whose eigenvalues are positive real numbers.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/1d157c853e3adf2f35a312dd80ccbfad31db8095
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In Computational Theory and Mathematics
In Geometry and Topology
In Statistical and Nonlinear Physics
Citations in the corpus
- Decentralized Consensus Control of a Rigid-Body Spacecraft Formation with Communication Delay (2016, background): “, no directed circles can be found in the digraph), then it can be shown that the algebraic and geometric means of the eigenvalues of the matrix IN A (where IN ∈ RN×N is the identity matrix of the same size as A) are equal, and hence all eigenvalues of IN A are equal to 1 [30].”