We consider the graphs whose edges are marked by the integers (weights) from$0$ to $q-1$ (zero corresponds to no-edge). Such graph is called additive ifits vertices can be marked in such a way that the weight of every edge is equalto the modulo-$q$ sum of weights of the two incident vertices. By a switchingof a graph we mean the modulo-$q$ sum of the graph with some additive graph onthe same vertex set. A graph with $n$ vertices is called switching separable ifsome of its switchings does not have a connected component of order $n$ or$n-1$. We consider the following test for the switching separability: ifremoving any vertex of a graph $G$ results in a switching separable graph, then$G$ is switching separable itself. We prove this test for odd $q$ andcharacterize the exceptions when $q$ is even. We establish a connection betweenthe switching separability of a graph and the reducibility of $(n-1)$-aryquasigroups constructed from this graph.
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机译：我们考虑图的边由从$ 0 $到$ q-1 $的整数（权重）标记（零表示无边）。如果这种图形的顶点可以以每个边的权重等于两个入射顶点的权重之和为模qq $的方式进行标记，则称为加法图。通过切换图，我们指的是图的模-$ q $和与在相同顶点集上的一些加法图。如果具有$ n $个顶点的图的某些切换没有顺序为$ n $或$ n-1 $的连通分量，则称该图为可分离切换。我们考虑对切换可分离性进行以下测试：如果删除图$ G $的任何顶点会导致切换可分离图，则$ G $本身就是切换可分离的。我们证明此测试适用于奇数$ q $并表征$ q $偶数时的异常。我们在图的切换可分离性和由该图构造的$（n-1）$-拟基的可约性之间建立联系。
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