The Wiener-type invariants of a simple connected graph G = (V(G), E(G)) can be expressed in terms of the quantities W f = {u,v}⊆V(G) f (d G (u, v)) for various choices of the function f (x), where d G (u, v) is the distance between vertices u and v in G. In this paper, we give some sufficient conditions for a bipartite graph to be Hamiltonian or a connected general graph to be Hamilton-connected and traceable from every vertex in terms of the Wiener-type invariants of G or the complement of G,