@article{Su2025, 
author = {Zhenhua Su},
title = {Extremal degree-based topological indices for trees with given segment number},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {11},
pages = {27677-27695},
keywords = {extremal values, topological indices, trees, segment number},
url = {https://www.sciopen.com/article/10.3934/math.20251217},
doi = {10.3934/math.20251217},
abstract = {A degree-based topological index of a tree    T is termed as     T      I    f    (  T  )  =      ∑                  v        1                    v        2            ∈      E      (      T      )        f  (  d  (      v    1    )  ,  d  (      v    2    )  )  ,in which    f  (  x  ,  y  )  =  f  (  y  ,  x  ) denotes a real-valued function with    x  ,  y  ≥  1. This paper mainly focuses on the extremal topological index problems for trees with a given segment number. We respectfully present the sufficient conditions for achieving the smallest and largest values of    T      I    f  , as well as depict the associated extremal graphs. As an application, it is verified that there are eight types of degree-based indices that meet these sufficient conditions, including the recently proposed Euler Sombor index and diminished Sombor index.}
}