The K1,2-structure-connectivity of graphs

n this paper, we mainly investigate K1,2-structure-connectivity for any connected graph. Let G be a connected graph with n vertices, we show that κ(G; K1,2) is well-defined if diam(G)≥ 4, or n≡ 1 3, or G∉ ₅,Kₙ\ when n≡ 2 3, or there exist three vertices $u,v,w$ such that NG(u)∩ (NG(v,w)∪,w\)=∅ when n≡ 0 3. Furthermore, if G has K1,2-structure-cut, we prove κ(G)/3≤κ(G; K1,2)≤κ(G).