An enumeration of graphical designs |
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| Authors: | Yeow Meng Chee Petteri Kaski |
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| Institution: | 1. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637616;2. Interactive Digital Media R&D Program Office, Media Development Authority, 140 Hill Street, Singapore 179369;3. Helsinki Institute for Information Technology HIIT, Department of Computer Science, University of Helsinki, P.O. Box 68, 00014 University of Helsinki, Finland |
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| Abstract: | Let Ψ(t,k) denote the set of pairs (v,λ) for which there exists a graphical t‐(v,k,λ) design. Most results on graphical designs have gone to show the finiteness of Ψ(t,k) when t and k satisfy certain conditions. The exact determination of Ψ(t,k) for specified t and k is a hard problem and only Ψ(2,3), Ψ(2,4), Ψ(3,4), Ψ(4,5), and Ψ(5,6) have been determined. In this article, we determine completely the sets Ψ(2,5) and Ψ(3,5). As a result, we find more than 270,000 inequivalent graphical designs, and more than 8,000 new parameter sets for which there exists a graphical design. Prior to this, graphical designs are known for only 574 parameter sets. © 2006 Wiley Periodicals, Inc. J Combin Designs 16: 70–85, 2008 |
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| Keywords: | combinatorial designs enumeration |
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