A Steiner general position problem in graph theory

Let G be a graph. The Steiner distance of $$W\subseteq V(G)$$ is the minimum size connected subgraph containing W. Such necessarily tree called W-tree. set $$A\subseteq k-Steiner general position if $$V(T_B)\cap A = B$$ holds for every $$B\subseteq A$$ cardinality k, and B-tree $$T_B$$ . number $$\mathrm{sgp}_k(G)$$ largest in G. cliques are introduced used to bound from below. determined trees, cycles joins graphs. Lower bounds presented split graphs, infinite grids lexicographic products. lower latter product leads an exact formula arbitrary product.