Classification of partially metric Q-polynomial association schemes with $m_1=4$

Abstract

We classify the Q-polynomial association schemes with $m_1=4$ which are partially metric with respect to the nearest neighbourhood relation. An association scheme is partially metric with respect to a relation $R_1$ if the scheme graph of $R_2$ is exactly the distance-2 graph of the scheme graph of $R_1$ under a certain ordering of the relations.

14 pages, 1 figure