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This is a Quantitative Study study.

September 23, 2025Open Access

Almost all cographs have a cospectral mate

WWWei WangUnion Hospital XHX. HuangNational University of Defense Technology

Puntos clave

Almost all cographs possess a cospectral mate, highlighting a significant property in graph theory.
This finding relies on the Johnson-Newman theorem and asymptotic enumeration techniques to establish its validity.
The result parallels Schwenk's work on trees, demonstrating a broader applicability in the study of graph properties.
Such connections can deepen our understanding of graph relationships and the structure of complement-reducible graphs.

Resumen

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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Cite This Study

Wang et al. (Tue,) studied this question.

synapsesocial.com/papers/68d4759931b076d99fa6daac https://doi.org/https://doi.org/10.48550/arxiv.2507.16730