3 papers
math.CO2025
Remarks on the Brouwer Conjecture
Oliver Knill
The Brouwer conjecture (BC) in spectral graph theory claims that the sum of the largest k Kirchhoff eigenvalues of a graph are bounded above by the number m of edges plus k(k+1)/2.…
math.CO2025
Soft Barycentric Refinement
Oliver Knill
The soft Barycentric refinement preserves manifolds with or without boundary. In every dimension larger than one, there is a universal spectral central limiting measure that has af…
nlin.SI2024
On Symmetries of Finite Geometries
Oliver Knill
The isospectral set of the Dirac matrix D=d+d* consists of orthogonal Q for which Q* D Q is an equivalent Dirac matrix. It can serve as the symmetry of a finite geometry G. The sym…