Degree Sum and Neighborhood Intersections for Hamilton-connection

Let S^23 denote an independent set with mini dist (u,v)|u, v∈S} = 2 and |S|=3. Our main result is the following theorem: Let G be a 3-connected graph of order n such that d(u)+d(v)+d(w)≥n+1+|N(u)∩N(v)∩N(w)|for any independent set S^23={u,v,w}, then G is Hamilton-connected.