Further criteria for the indecomposability of finite pseudometric spaces

We continue the study of indecomposable finite (consisting of a finite number of points) pseudometric spaces (i.e., spaces whose only decomposition into a sum is the division of all distances in equal proportion). We prove that the indecomposability property is invariant under the following operation: connect two disjoint points by an additional simple chain, which is the inverted copy of the shortest path connecting these points. The indecomposability of the spaces presented by the graphsK _m,n (m ≥ 2,n ≥ 3) with edges of equal length is also proved. Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 421–424, March, 1998.