On the asymptotic behavior of graphs determined by their generalized spectra

In Wang and Xu (2006) [15,16] the authors introduced a family of graphs H n and gave some methods for finding graphs among this family that are determined by their generalized spectra. This paper is a continuation of our previous work. We further show that almost all graphs in H n are determined by their generalized spectra. This gives some evidences for the conjecture that almost all graphs are determined by their generalized spectra.