On the general atom-bond sum-connectivity index

This paper is concerned with a generalization of the atom-bond sum-connectivity (ABS) index, devised recently in [A. Ali, B. Furtula, I. Redžepović, I. Gutman, Atom-bond sum-connectivity index, J. Math. Chem., 60 (2022), 2081-2093]. For a connected graph G with an order greater than $ 2 $, the general atom-bond sum-connectivity index is represented as ABS_γ(G) and is defined as the sum of the quantities (1-2(dₓ+dy)⁻¹)γ over all edges $ xy $ of the graph G, where dₓ and dy represent the degrees of the vertices x and y of G, respectively, and γ is any real number. For -10≤ γ ≤ 10, the significance of ABS_γ is examined on the data set of octane isomers for predicting six selected physicochemical properties of the mentioned compounds; promising results are obtained when the approximated value of γ belongs to the set \-3, 1, 3\. The effect of the addition of an edge between two non-adjacent vertices of a graph under ABS_γ is also investigated. Moreover, the graphs possessing the maximum value of ABSγ, with γ > 0, are characterized from the set of all connected graphs of a fixed order and a fixed (ⅰ) vertex connectivity not greater than a given number or (ⅱ) matching number.