An Enumeration of Graphical Designs
| dc.creator | Chee, Yeow Meng | |
| dc.creator | Kaski, Petteri | |
| dc.date | 2007-12-23 | |
| dc.date.accessioned | 2026-07-07T08:51:09Z | |
| dc.date.available | 2026-07-07T08:51:09Z | |
| dc.description | 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 paper, we determine completely the sets $Ψ(2,5)$ and $Ψ(3,5)$. As a result, we find more than 270000 inequivalent graphical designs, and more than 8000 new parameter sets for which there exists a graphical design. Prior to this, graphical designs are known for only 574 parameter sets. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/0712.3895 | |
| dc.identifier | http://arxiv.org/abs/0712.3895 | |
| dc.identifier | Journal of Combinatorial Designs, vol. 16, no. 1, pp. 70-85, 2008 | |
| dc.identifier | doi:10.1002/jcd.20137 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144837 | |
| dc.subject | Combinatorics | |
| dc.title | An Enumeration of Graphical Designs | |
| dc.type | text |