Maximal $m$-distance sets containing the representation of the Johnson graph $J(n,m)$

Abstract

We classify the maximal $m$-distance sets in ${\mathbb{R}}^{n-1}$ which contain the representation of the Johnson graph $J(n,m)$ for $m=2,3$. Furthermore, we determine the necessary and sufficient condition for $n$ and $m$ such that the representation of the Johnson graph $J(n,m)$ is not maximal as an $m$-distance set. Also, we classify the maximal two-distance sets in ${\mathbb{R}}^{n-1}$ which contain the representation of $J(n-1,2)$.

10 pages, http://researchmap.jp/j_shigezumi/ESSP2009/ (in Japanese)

References in corpus (1)

• Uniqueness of maximum three-distance sets in the three-dimensional Euclidean space

Cited by in corpus (1)

• Maximal $m$-distance sets containing the representation of the Hamming graph $H(n,m)$