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The Koolen–Park Boundary and Distance-Regular Graphs without m-Claws

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Abstract

J.H. Koolen and J. Park found a boundary for the maximum size of the coclique in the neighborhood of a vertex of a distance-regular graph. Using this boundary, we prove that distance-regular graphs with the intersection arrays {83, 54, 21; 1, 6, 63}, {80, 54, 12; 1, 6, 60}, and {93, 64, 24; 1, 12, 62} do not exist.

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Funding

This work was financially supported by the Russian Foundation for Basic Research and the National Natural Science Foundation of China (project no. 20-51-53013), along with the National Natural Science Foundation of China (project no. 12171126).

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Authors and Affiliations

  1. School of Science, Hainan University, 570228, Haikou, Hainan, China

    A. A. Makhnev & Wenbin Guo

  2. Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, 620137, Yekaterinburg, Russia

    A. A. Makhnev & K. S. Efimov

  3. University of Science and Technology of China, 230026, Hefei, China

    Wenbin Guo

  4. Ural State Mining University, 620144, Yekaterinburg, Russia

    K. S. Efimov

  5. Ural Federal University, 620002, Yekaterinburg, Russia

    K. S. Efimov

Authors
  1. A. A. Makhnev
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  2. Wenbin Guo
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  3. K. S. Efimov
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Corresponding authors

Correspondence to A. A. Makhnev, Wenbin Guo or K. S. Efimov.

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The authors declare that they have no conflicts of interest.

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Translated by L. Kartvelishvili

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Makhnev, A.A., Guo, W. & Efimov, K.S. The Koolen–Park Boundary and Distance-Regular Graphs without m-Claws. Russ Math. 66, 54–57 (2022). https://doi.org/10.3103/S1066369X22090067

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  • DOI: https://doi.org/10.3103/S1066369X22090067

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