Geodesic
Further criteria for the indecomposability of finite pseudometric spaces
Matematičeskie zametki, Tome 63 (1998) no. 3, pp. 421-424

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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 graphs $K_{m,n}$ ($m\ge2$, $n\ge3$) with edges of equal length is also proved. 
@article{MZM_1998_63_3_a12,
     author = {M. \'E. Mikhailov},
     title = {Further criteria for the indecomposability of finite pseudometric spaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {421--424},
     publisher = {mathdoc},
     volume = {63},
     number = {3},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_3_a12/}
}
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M. É. Mikhailov. Further criteria for the indecomposability of finite pseudometric spaces. Matematičeskie zametki, Tome 63 (1998) no. 3, pp. 421-424. http://geodesic.mathdoc.fr/item/MZM_1998_63_3_a12/