Computing the szeged, revised szeged and normalized revised szeged indices of the polycyclic aromatic hydrocarbons PAHk

The aim in this paper is to computing the Szeged Index (the vertex version) and its two new versions (the revised Szeged index and the normalized revised Szeged index) of the Polycyclic Aromatic Hydrocarbons PAHk. Let G be a connected graph. The vertex-set and edge-set of G denoted by V (G) and E(G) respectively. The distance between the vertices u and v, d(u, v), in a graph is the number of edges in a shortest path connecting them. The Szeged index of the graph G is defined as Sz(G) = e ∈ E(G)[nu(e , G) × nv (e, G)], where nu(e , G) = {x , x ∈ V(G), d(u,x) < d(x,v)}and nv(e , G)= {x , x ∈ V(G), d(v,x) < d( x,u)}.