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2-Reconstructibility of Strongly Regular Graphs and 2-Partially Distance-Regular Graphs

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Abstract

A graph is \(\ell \)-reconstructible if it is determined by its multiset of induced subgraphs obtained by deleting \(\ell \) vertices. For graphs with at least six vertices, we prove that all graphs in a family containing all strongly regular graphs and most 2-partially distance-regular graphs are 2-reconstructible.

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Acknowledgements

We thank Alexandr V. Kostochka for helpful discussions and Edwin van Dam for pointing out the equivalence between weakly distance-regular and 2-partially distance-regular graphs.

Funding

Research of Douglas B. West was supported by National Natural Science Foundation of China grants NSFC 11871439, 11971439, and U20A2068. Research of Xuding Zhu was supported by National Natural Science Foundation of China grants NSFC 11971438 and U20A2068.

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Authors and Affiliations

  1. Zhejiang Normal University, Jinhua, China

    Douglas B. West & Xuding Zhu

  2. University of Illinois at Urbana–Champaign, Urbana, IL, USA

    Douglas B. West

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  1. Douglas B. West
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  2. Xuding Zhu
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As is standard in mathematical papers, all authors contributed fully to the paper.

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Correspondence to Douglas B. West.

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West, D.B., Zhu, X. 2-Reconstructibility of Strongly Regular Graphs and 2-Partially Distance-Regular Graphs. Graphs and Combinatorics 39, 94 (2023). https://doi.org/10.1007/s00373-023-02693-1

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  • DOI: https://doi.org/10.1007/s00373-023-02693-1

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