The generalized graph spectrum is the pair consisting of the graph spectrum of a graph and that of its graph complement. A graph is determined by its generalized spectrum if every graph with the same pair of spectra is isomorphic to it.
Xiang (2026) reported that a random graph sampled from 
is determined by its generalized spectrum with probability
tending to 1 as 
.
This is a weaker statement than the Haemers conjecture,
which uses only the spectrum of the graph itself.
