Browsing by Author "Çelik, Derya"
Now showing items 12 of 2

An equivalence class decomposition of finite metric spaces via Gromov products
Authors:Bilge, Ayşe Hümeyra; Çelik, Derya; Koçak, Şahin
Publisher and Date:(Elsevier Science Bv, 2017)Let (X, d) be a finite metric space with elements Pi, i = 1,..., n and with the distance functions d(ij) The Gromov Product of the "triangle" (Pi, Pj, Pk) with vertices Pt, Pj and Pk at the vertex Pi is defined by Delta(ijk) = 1/2(d(ij) + d(ik)  d(jk)). We show that the collection of Gromov products determines the metric. We call a metric space Deltageneric, if the set of all Gromov products at a fixed vertex Pi has a unique smallest element (for i = 1,., n). We consider the function ...

Gromov product structures, quadrangle structures and split metric spaces
Authors:Bilge, Ayşe Hümeyra; Çelik, Derya; Koçak, Şahin; Rezaeinazhad, Arash Mohammadian
Publisher and Date:(Elsevier B.V., 202106)Let (X,d) be a finite metric space with elements Pi, i=1,…,n and with distances dij≔d(Pi,Pj) for i,j=1,…,n. The “Gromov product” Δijk, is defined as [Formula presented]. (X,d) is called Δgeneric, if, for each fixed i, the set of Gromov products Δijk has a unique smallest element, Δijiki. The Gromov product structure on a Δgeneric finite metric space (X,d) is the map that assigns the edge Ejiki to Pi. A finite metric space is called “quadrangle generic”, if for all 4point subsets {Pi,Pj,Pk,Pl}, ...