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arXiv · 2507.16730

Almost all cographs have a cospectral mate

Wei Wang·Ximei Huang
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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.

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Wei Wang, Ximei Huang. 2025-07-22. Almost all cographs have a cospectral mate. https://arxiv.org/abs/2507.16730

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