Further criteria for the indecomposability of finite pseudometric spaces |
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Authors: | M. É. Mikhailov |
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Affiliation: | (1) Institute of Genetics, Moldovian Academy of Sciences, Kishinev |
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Abstract: | 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. |
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Keywords: | pseudometric spaces graphs indecomposability |
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