The K_1,2-structure-connectivity of graphs

n this paper, we mainly investigate K_1,2-structure-connectivity for any connected graph. Let G be a connected graph with n vertices, we show that κ(G; K_1,2) is well-defined if diam(G)≥ 4, or n≡ 1 3, or G∉{C_5,K_n} when n≡ 2 3, or there exist three vertices u,v,w such that N_G(u)∩ (N_G(v,w)∪{v,w})=∅ when n≡ 0 3. Furthermore, if G has K_1,2-structure-cut, we prove κ(G)/3≤κ(G; K_1,2)≤κ(G).