An Enumeration of Graphical Designs - Mathematics > Combinatorics

Abstract: Let $\Psit,k$ denote the set of pairs $v,\lambda$ for which there existsa graphical $t$-$v,k,\lambda$ design. Most results on graphical designs havegone to show the finiteness of $\Psit,k$ when $t$ and $k$ satisfy certainconditions. The exact determination of $\Psit,k$ for specified $t$ and $k$ isa hard problem and only $\Psi2,3$, $\Psi2,4$, $\Psi3,4$, $\Psi4,5$, and$\Psi5,6$ have been determined. In this paper, we determine completely thesets $\Psi2,5$ and $\Psi3,5$. As a result, we find more than 270000inequivalent graphical designs, and more than 8000 new parameter sets for whichthere exists a graphical design. Prior to this, graphical designs are known foronly 574 parameter sets.

Author: Yeow Meng Chee, Petteri Kaski

Source: https://arxiv.org/