Abstract
In this paper, we classify all commutative weakly distance-regular digraphs of girth g and one type of arcs under the assumption that \(p_{(1,g-1),(1,g-1)}^{(2,g-2)}\ge k_{1,g-1}-2\). In consequence, Yang et al. (J Comb Theory Ser A 160:288–315, 2018, Theorem 1.1) is partially generalized by our result.
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Acknowledgements
The authors would like to thank the anonymous reviewers for their careful reading of the manuscript of the paper and their invaluable suggestions.
Funding
Y. Yang is supported by NSFC (12101575) and the Fundamental Research Funds for the Central Universities (Grant No. 2652019319), Z. Wang is supported by the Fundamental Research Funds for the Central Universities (Grant No. 2652019319).
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Fan, Y., Wang, Z. & Yang, Y. Weakly Distance-Regular Digraphs of One Type of Arcs. Graphs and Combinatorics 38, 89 (2022). https://doi.org/10.1007/s00373-022-02493-z
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DOI: https://doi.org/10.1007/s00373-022-02493-z