On the variable Wiener–Szeged inequality

In this note, we use a technique introduced by Klavžar et al. (1996) to obtain a strengthening of well-known inequality between the Szeged and Wiener indices. To be more precise, we will prove that if G is a connected graph and α>1, then ∑e=uv∈E(G)(ne(u)ne(v))α≥∑{u,v}⊆V(G)d(u,v)α and equality holds if and only if G is complete.