Graphs and Combinatorics

, Volume 2, Issue 1, pp 15–20 | Cite as

Symmetry and classification of certain regular group divisible designs

  • Bhagwandas
  • Sanpei Kageyama
  • Rahul Mukerjee
Article

Abstract

In this paper it is shown that a regular group divisible (GD) design, with parametersv, b, r, k, λ1, λ2 satisfyingrk − λ2v + 1 andλ2 = λ1 + 1, must be symmetric (i.e.,v + b). Furthermore, the parameters of such symmetric regular GD designs can be expressed in terms of only two integral parameters.

Keywords

Integral Parameter Group Divisible Regular Group Group Divisible Design 

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References

  1. 1.
    Clatworthy, W.H.: Tables of Two-Associate-Class Partially Balanced Designs. Applied Mathematics Series 63. Washington, D.C.: NBS 1973Google Scholar
  2. 2.
    John, J.A., Turner, G.: Some new group divisible designs. J. Stat. Plann. Inference1, 103–107 (1977)Google Scholar
  3. 3.
    Raghavarao, D.: Constructions and Combinatorial Problems in Design of Experiments. New York: John Wiley & Sons 1971Google Scholar
  4. 4.
    Shrikhande, S.S.: Affine resolvable balanced incomplete block designs; a survey. Aequationes Math.14, 251–269 (1976)Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Bhagwandas
    • 1
  • Sanpei Kageyama
    • 2
  • Rahul Mukerjee
    • 3
  1. 1.Department of StatisticsUniversity of IndoreIndoreIndia
  2. 2.Department of MathematicsHiroshima UniversityHiroshimaJapan
  3. 3.Indian Statistical Institute and Hiroshima UniversityJapan

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