Abstract
Let (G,w) be a network, that is, a graph G=(V(G),E(G)) together with the weight function w:E(G)→R+. The Szeged index Sz(G,w) of the network (G,w) is introduced and proved that Sz(G,w)≥W(G,w) holds for any connected network where W(G,w) is the Wiener index of (G,w). Moreover, equality holds if and only if (G,w) is a block network in which w is constant on each of its blocks. Analogous result holds for vertex-weighted graphs as well.
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