Further criteria for the indecomposability of finite pseudometric spaces (Q1280690)

From the summary (translation): The author continues his investigation of the criteria for finite indecomposable pseudometric spaces, which cannot be decomposed into a sum except by partition of all distances in equal proportion [the author, Math. Notes 63, No. 2, 225-234 (1998); translation from Mat. Zametki 63, No. 2, 197-204 (1998; Zbl 0944.54022)]. It is proved that indecomposability is preserved if in the graph, representing the space, two vertices, not connected by an edge, are connected by an additional simple chain which is a copy of the shortest sequence connecting these vertices but which is joined at opposite ends. It is also proved that the spaces being represented by the graphs \(K_{m,n}\) \((m\geq 2,n\geq 3)\) with edges of equal length are indecomposable.