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An enumeration of graphical designs

✍ Scribed by Yeow Meng Chee; Petteri Kaski

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
183 KB
Volume
16
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

Let Ξ¨(t,k) denote the set of pairs (v,Ξ») for which there exists a graphical t‐(v,k,Ξ») design. Most results on graphical designs have gone to show the finiteness of Ξ¨(t,k) when t and k satisfy certain conditions. The exact determination of Ξ¨(t,k) for specified t and k is a hard problem and only Ξ¨(2,3), Ξ¨(2,4), Ξ¨(3,4), Ξ¨(4,5), and Ξ¨(5,6) have been determined. In this article, we determine completely the sets Ξ¨(2,5) and Ξ¨(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. Β© 2006 Wiley Periodicals, Inc. J Combin Designs 16: 70–85, 2008

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