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On the Automorphism Group of the Substructure Ordering of Finite Directed Graphs

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Abstract

We investigate the automorphism group of the substructure ordering of finite directed graphs. The second author conjectured that it is isomorphic to the 768-element group \((\mathbb {Z}_2^4 \times S_4)\rtimes _{\alpha } \mathbb {Z}_2\). Though unable to prove it, we solidify this conjecture by showing that the automorphism group behaves as expected by the conjecture on the first few levels of the poset in question. With the use of computer calculation we analyze the first four levels holding 3160 directed graphs.

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Funding

This research was supported by project TKP2021-NVA-09. Project no. TKP2021-NVA-09 has been implemented with the support provided by the Ministry of Innovation and Technology of Hungary from the National Research, Development and Innovation Fund, financed under the TKP2021-NVA funding scheme. The second author was supported by the National Research, Development and Innovation Office (Hungary), Grants K128042 and K138892.

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Authors and Affiliations

  1. ELKH-SZTE Analysis and Applications Research Group, Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H–6720, Szeged, Hungary

    Fanni K. Nedényi

  2. Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720, Szeged, Hungary

    Ádám Kunos

Authors
  1. Fanni K. Nedényi
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  2. Ádám Kunos
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Both authors have contributed equally to the work.

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Correspondence to Ádám Kunos.

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Nedényi, F.K., Kunos, Á. On the Automorphism Group of the Substructure Ordering of Finite Directed Graphs. Order (2023). https://doi.org/10.1007/s11083-023-09642-w

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  • DOI: https://doi.org/10.1007/s11083-023-09642-w

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