@article{Alraqad2024, 
author = {Tariq A. Alraqad and Igor Ž. Milovanović and Hicham Saber and Akbar Ali and Jaya P. Mazorodze and Adel A. Attiya},
title = {Minimum atom-bond sum-connectivity index of trees with a fixed order and/or number of pendent vertices},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {2},
pages = {3707-3721},
keywords = {topological index, atom-bond sum-connectivity, tree},
url = {https://www.sciopen.com/article/10.3934/math.2024182},
doi = {10.3934/math.2024182},
abstract = {Let        d    u   be the degree of a vertex    u of a graph    G. The atom-bond sum-connectivity (ABS) index of a graph    G is the sum of the numbers    (  1  −  2  (      d    v    +      d    w        )          −      1            )          1              /            2       over all edges    v  w of    G. This paper gives the characterization of the graph possessing the minimum ABS index in the class of all trees of a fixed number of pendent vertices; the star is the unique extremal graph in the mentioned class of graphs. The problem of determining graphs possessing the minimum ABS index in the class of all trees with    n vertices and    p pendent vertices is also addressed; such extremal trees have the maximum degree    3 when    n  ≥  3  p  −  2  ≥  7, and the balanced double star is the unique such extremal tree for the case    p  =  n  −  2.}
}