Almost all cographs have a cospectral mate
Combinatorics
2025-07-23 v1
Abstract
Complement-reducible graphs (or cographs) are the graphs formed from the single-vertex graph by the operations of complement and disjoint union. By combining the Johnson-Newman theorem on generalized cospectrality with the standard tools in the asymptotic enumeration of trees, we show that almost all cographs have a cospectral mate. This result can be viewed as an analogue to a well-known result by Schwenk, who proved that almost all trees have a cospectral mate.
Cite
@article{arxiv.2507.16730,
title = {Almost all cographs have a cospectral mate},
author = {Wei Wang and Ximei Huang},
journal= {arXiv preprint arXiv:2507.16730},
year = {2025}
}
Comments
12 pages, 4 figures