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. Redz ˇepovie, 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 & gamma;(G) and is defined as the sum of the quantities (1 - 2(dx + dy)-1)& gamma; 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 & gamma; is any real number. For -10 < & gamma; < 10, the significance of ABS & gamma; 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 & gamma; 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 & gamma; is also investigated. Moreover, the graphs possessing the maximum value of ABS & gamma;, with & gamma; > 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.