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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.CO2025
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…