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.

中文翻译：

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$$ m_ {1} = 4 $$ m 1 = 4的部分度量Q多项式关联方案的分类

我们将\（m_ {1} = 4 \）的Q多项式关联方案分类为关于最近邻关系的部分度量。的关联方案是相对于的关系部分地度量\（R_1 \）如果的方案图表\（R_2 \）是完全的方案图的距离-2图表\（R_1 \）的关系的一定的顺序下。