Alexander Van Werde

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20242026

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math.CO2026

Are sparse graphs typically determined by their spectrum?

Nils Van de Berg, Alexander Van Werde

We investigate whether it is typical for a sparse graph to be uniquely characterized by its adjacency spectrum up to isomorphism. Our first result shows that the giant component of…

math.CO2026

A sufficient condition for generalized spectral characterization of graphs with loops

Alexander Van Werde

Sufficient conditions for a simple graph to be characterized up to isomorphism given its spectrum and the spectrum of its complement graph are known due to Wang and Xu. This note e…

math.CO2025

Cokernel statistics for walk matrices of directed and weighted random graphs

Alexander Van Werde

The walk matrix associated to an $n \times n$ integer matrix $X$ and an integer vector $b$ is defined by $W := (b, X b, ..., X^{n - 1} b)$ . We study limiting laws for the cokernel of…