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PBIB-Designs from Certain Subsets of Distance-Regular Graphs

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Abstract

Partially balanced incomplete block (PBIB)-designs are well known to be the generalization of combinatorial 2-designs. In this paper, we first construct PBIB-designs from diametral paths of distance-regular graphs, which generalizes the result for strongly regular graphs. Furthermore, for Q-polynomial distance-regular graphs associated with regular semilattices, we obtain the construction of PBIB-designs through descendents with fixed dual width.

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Acknowledgements

The authors sincerely thank the anonymous referees for pointing out errors and many valuable suggestions to improve our results. Yan Zhu is supported by National Natural Science Foundation of China No. 11801353 and the Fundamental Research Funds for the Central Universities.

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Authors and Affiliations

  1. College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Nan Li & Yan Zhu

  2. Ministry of Education Funded Key Laboratory of Scientific and Engineering Computing, Shanghai Jiao Tong University, Shanghai, 200240, China

    Yan Zhu

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  1. Nan Li
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  2. Yan Zhu
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Correspondence to Yan Zhu.

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Communicated by Ebrahim Ghorbani.

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Li, N., Zhu, Y. PBIB-Designs from Certain Subsets of Distance-Regular Graphs. Bull. Iran. Math. Soc. 50, 15 (2024). https://doi.org/10.1007/s41980-024-00859-y

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  • DOI: https://doi.org/10.1007/s41980-024-00859-y

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