@article{Albalahi2023, 
author = {Abeer M. Albalahi and Zhibin Du and Akbar Ali},
title = {On the general atom-bond sum-connectivity index},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {10},
pages = {23771-23785},
keywords = {topological index, chemical graph theory, atom-bond sum-connectivity, general atom-bond sum-connectivity},
url = {https://www.sciopen.com/article/10.3934/math.20231210},
doi = {10.3934/math.20231210},
abstract = {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    A  B      S    γ    (  G  ) and is defined as the sum of the quantities    (  1  −  2  (      d    x    +      d    y        )          −      1            )          γ       over all edges    x  y of the graph    G, where        d    x   and        d    y   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    A  B      S    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    A  B      S    γ   is also investigated. Moreover, the graphs possessing the maximum value of    A  B      S          γ      , 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.}
}