The edge version of the Szeged index - Gutman, Ivan (Array, 2008)
Summary: The Szeged index is a molecular structure descriptor equal to the sum of products nu(e đ G) ⋅ nn(e | G) over all edges e = (uv) of the molecular graph G, where nu(e | G) is the number of vertices whose distance to vertex u is smaller than the distance to vertex v, and where nv(e | G) is defined analogously. We now examine the edge version of the Szeged index: the sum of products mu(e | G)∙mv(e | G) over all edges e = (uv) of the molecular graph G, where mu(e | G) is the number of edges whose distance to vertex u is smaller than the distance to vertex v, and where mv(e | G) is defined analogously. The basic properties of this novel structure descriptor are established. Most of these are analogous to the properties of the ordinary Szeged index, but some remarkable differences are also recognized