Bulletin of the
Korean Mathematical Society BKMS

Let $(\Omega,S)$ be an association scheme where $\Omega$ is a non-empty finite set and $S$ is a partition of $\Omega\times\Omega$. For a positive integer $k$ we say that $(\Omega,S)$ is {\it $k$-equivalenced} if each non-diagonal element of $S$ has valency $k$. In this paper we focus on $4$-equivalenced association schemes, and prove that they are transitive.

Keywords: association schemes, equivalenced, Frobenius, schurian, transitive

MSC numbers: 05E30