On revised Szeged index of graphs - Shabani, Hossein; Ashrafi, Ali Reza; Gutman, Ivan (Utilitas Mathematica, 2014)
The revised Szeged index Sz∗(G) is a graph invariant, used as molecular structure descriptor, equal to the sum of products [nu(e) + n0(e)/2]∼ es;[nv(e) + n0(e)/2] over all edges e = uv of a graph G, where n0(e) is the number of vertices equidistant to u and v, nu (e) is the number of vertices whose distance to vertex u is smaller than the distance to vertex v and nv(e) is defined analogously. A new formula for computing Sz∗ (G) is presented. The relationships between Sz∗(G), vertex PI index, and second Zagreb index are also investigated.