Combinatorial structure of group divisible designs without α-resolution classes in each group

  • Authors:

  • Tomoko Adachi;Masakazu Jimbo;Sanpei Kageyama

  • Affiliations:

  • Department of Mathematics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan;Department of Mathematics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan;Department of Mathematics, Hiroshima University, 1-1-1, Kagamiyama, Higashi-Hiroshima 739-8524, Japan

  • Venue:
  • Discrete Mathematics
  • Year:
  • 2003

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Abstract

It is known that group divisible designs (GDDs) with r = λ1 + 1 are regular and symmetric, and that the combinatorial structure of these designs is characterized in terms of Hadamard tournaments and strongly regular graphs. In this paper, it is shown that GDDs without α-resolution classes in each group are also specified by Hadamard tournaments and strongly regular graphs. The result given by Jimbo and Kageyama (ICA Bull. 32 (2001) 29) is included in the present result as a special case.