Year: 2026
Type: preprint
Abstract: We present a proof of the two-token graph reconstruction conjecture. Every finite simple graph $G,H$ of order at least three, $F_2(G) \cong F_2(H)$ if and only if $G \cong H$. We also classify the automorphism groups of two-token graphs whose connected roots have order at least five. Combining these results, we show that, for connected graphs $G,H$ of order at least five, every isomorphism $ϕ:F_2(G)\to F_2(H)$ admits a factorization $ϕ=η\circσ^{(2)}$, where $σ^{(2)}$ is induced by a graph isomorphism $σ:G\to H$, and $η\in \operatorname{Aut}(F_2(H))$ is a product of twin-cut switches or Cartesian exchanges.
Source: arXiv (Cornell University)
Authors: Luo, Yuanming, Hu, Hao
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221775025