On revised Szeged index of graphs

Abstract

The revised Szeged index S_z^∗(G) is a graph invariant, used as molecular structure descriptor, equal to the sum of products [n_u(e) + n₀(e)/2]∼ es;[n_v(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, n_u (e) is the number of vertices whose distance to vertex u is smaller than the distance to vertex v and n_v(e) is defined analogously. A new formula for computing S_z^∗ (G) is presented. The relationships between S_z^∗(G), vertex PI index, and second Zagreb index are also investigated.