@article{Ali2024, 
author = {Akbar Ali and Sneha Sekar and Selvaraj Balachandran and Suresh Elumalai and Abdulaziz M. Alanazi and Taher S. Hassan and Yilun Shang},
title = {Graphical edge-weight-function indices of trees},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {11},
pages = {32552-32570},
keywords = {topological index, graphical edge-weight-function index, Euler-Sombor index, tree graph, bound},
url = {https://www.sciopen.com/article/10.3934/math.20241559},
doi = {10.3934/math.20241559},
abstract = {Consider a tree graph  G with edge set  E(G). The notation  dG(x) represents the degree of vertex  x in  G. Let  f be a symmetric real-valued function defined on the Cartesian square of the set of all distinct elements of the degree sequence of  G. A graphical edge-weight-function index for the graph  G, denoted by  If(G), is defined as  If(G)=∑st∈E(G)f(dG(s),dG(t)). This paper establishes the best possible bounds for  If(G) in terms of the order of  G and parameter  p, subject to specific conditions on  f. Here,  p can be one of the following three graph parameters: (ⅰ) matching number, (ⅱ) the count of pendent vertices, and (ⅲ) maximum degree. We also characterize all tree graphs that achieve these bounds. The constraints considered for  f are satisfied by several well-known indices. We specifically illustrate our findings by applying them to the recently introduced Euler-Sombor index.}
}