The automorphisms of 2-token graphs

Ju Zhang, Jin-Xin Zhou, Yan-Tao Li and Young Soo Kwon

Applied Mathematics and Computation, 2023, vol. 446, issue C

Abstract: Let Λ=(V(Λ),E(Λ)) be a graph. The 2-token graphF2(Λ) of Λ is with vertex set all the 2-subsets of V(Λ), a pair of 2-subsets are adjacent if the symmetric difference is exactly in E(Λ). In this paper, it is proved that Z2n−1⋊Aut(Λ)≲Aut(F2(Λ)), where Λ is a Cartesian product of n prime graphs. Then it is shown that the equality may happen by proving that Aut(F2(Qn))≅Z2n−1⋊Aut(Qn), where Qn is the n-dimensional hypercube with n≥3. This also provides some partial answers to [25, Problem 1.3].

Keywords: 2-token graphs; Hypercube; Automorphism group (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:446:y:2023:i:c:s0096300323000413

DOI: 10.1016/j.amc.2023.127872

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