Szeged Indices of Bicyclic Graphs with Applications as Molecular Descriptor

Molecular descriptors are mathematical representations of molecular properties, generated through numerous algorithms. These numerical values are used to quantitatively represent the physical and chemical attributes of molecules. In the field of chemical graph theory, two indices, namely the revised Szeged index and the revised edge-Szeged index, were introduced to characterize molecular properties. The Szeged index Sz(Γ) of a simple connected graph Γ is computed by summing the products of nu(e) and nv (e)for all edges e = uv in Γ, where nu(e)denotes the number of vertices in Γ that are closer to vertex u than to vertex v, and nv (e) is defined similarly. In this paper, the role of different variants of Szeged indices in modeling different physical properties of alkanes and benzenoid hydrocarbon is investigated. Their isomer discrimination ability is also examined. In addition, we obtain lower and upper bounds on revised Szeged index, revised edge-Szeged index and the difference between vertex-edge Szeged index and edge-vertex Szeged index of bicyclic graphs.