Quasi-thin weakly distance-regular digraphs

  • Yuefeng Yang
  • Benjian Lv
  • Kaishun Wang


A weakly distance-regular digraph is quasi-thin if the maximum value of its intersection numbers is 2. In this paper, we focus on commutative quasi-thin weakly distance-regular digraphs, and classify such digraphs with valency more than 3. As a result, this family of digraphs is completely determined.


Weakly distance-regular digraph Quasi-thin Cayley digraph 

Mathematics Subject Classification




Y. Yang is supported by the Fundamental Research Funds for the Central Universities (Grant No. 2652017141), B. Lv is supported by NSFC (11501036), and K. Wang is supported by NSFC (11671043).


  1. 1.
    Arad, Z., Fisman, E., Muzychuk, M.: Generalized table algebras. Israel J. Math. 114, 29–60 (1999)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bannai, E., Ito, T.: Algebraic Combinatorics I: Association Schemes. Benjamin/Cummings, California (1984)zbMATHGoogle Scholar
  3. 3.
    Hanaki, A.: Classification of weakly distance-regular digraphs with up to 21 vertices, (2000)
  4. 4.
    Hirasaka, M.: On quasi-thin association schemes with odd number of points. J. Algebra 240, 665–679 (2001)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Hirasaka, M., Muzychuk, M.: On quasi-thin association schemes. J. Combin. Theory Ser. A 98, 17–32 (2002)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Muzychuk, M., Ponomarenko, I.: On quasi-thin association schemes. J. Algebra 351, 467–489 (2012)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Suzuki, H.: Thin weakly distance-regular digraphs. J. Combin. Theory Ser. B 92, 69–83 (2004)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Wang, K., Suzuki, H.: Weakly distance-regular digraphs. Discret. Math. 264, 225–236 (2003)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Wang, K.: Commutative weakly distance-regular digraphs of girth 2. Eur. J. Combin. 25, 363–375 (2004)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Yang, Y., Lv, B., Wang, K.: Weakly distance-regular digraphs of valency three, I. Electron. J. Combin. 23(2) (2016), Paper 2.12Google Scholar
  11. 11.
    Yang, Y., Lv, B., Wang, K.: Weakly distance-regular digraphs of valency three, II. J. Combin. Theory Ser. A 160, 288–315 (2018)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Zieschang, P.H.: An Algebraic Approach to Association Schemes. In: Lecture Notes in Mathematics, vol. 1628. Springer, Berlin, Heidelberg (1996)Google Scholar
  13. 13.
    Zieschang, P.H.: Theory of Association Schemes. Springer, Berlin (2005)zbMATHGoogle Scholar

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Authors and Affiliations

  1. 1.School of ScienceChina University of GeosciencesBeijingChina
  2. 2.School of Mathematical Sciences & Laboratory of Mathematics and Complex SystemsBeijing Normal UniversityBeijingChina

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