Abstract. Wiener index W(G) is the sum of distances over all pairs of vertices in the graph G. Gutman index Gut(G) is obtained analogously, just every term in the sum is the distance multiplied by the degrees of the vertices. Finally, edge-Wiener index We(G) is the Wiener index of the line graph of G.

In the paper we prove We(G) ≥ 1/4 Gut(G) - 1/4 |E(G)| + 3/4 k3(G) + 3 k4(G), where km(G) denotes the number of m-cliques in G.