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arXiv · 1202.1352

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

Eiichi Bannai·Takahiro Sato·Junichi Shigezumi
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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 $J(n - 1, 2)$.

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Eiichi Bannai, Takahiro Sato, Junichi Shigezumi. 2012-09-02. Maximal $m$-distance sets containing the representation of the Johnson graph $J(n, m)$. https://doi.org/10.1016/j.disc.2012.07.028

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