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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 with an order greater than , the general atom-bond sum-connectivity index is represented as and is defined as the sum of the quantities over all edges of the graph , where and represent the degrees of the vertices and of , respectively, and is any real number. For , the significance of 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 belongs to the set . The effect of the addition of an edge between two non-adjacent vertices of a graph under is also investigated. Moreover, the graphs possessing the maximum value of , 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