@article{Ali2025, 
author = {Akbar Ali and Darko Dimitrov and Tamás Réti and Abdulaziz Mutlaq Alotaibi and Abdulaziz M. Alanazi and Taher S. Hassan},
title = {Degree-based graphical indices of    k-cyclic graphs},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {6},
pages = {13540-13554},
keywords = {graphical index, bond incident degree index, Euler-Sombor index, elliptic Sombor index, Zagreb-Sombor index, topological index, k-cyclic graph},
url = {https://www.sciopen.com/article/10.3934/math.2025609},
doi = {10.3934/math.2025609},
abstract = {Let    G be a graph with edge set    E  (  G  ). Let        d    x   denote the degree of a vertex    x in    G. For a nonnegative integer    k, a connected graph of order    n and size    n  +  k  −  1 is called a    k-cyclic graph. This paper is concerned with    k-cyclic graphs and their graphical indices of the form    B  I      D          f        (  G  )  =      ∑          u      v      ∈      E      (      G      )        f  (      d    u    ,      d    v    ), where    f is a symmetric function whose outputs are real numbers. Particularly, the graphs minimizing or maximizing    B  I      D          f       among all    k-cyclic graphs with a given order are studied under certain constraints on    f. Various existing indices meet these constraints, and hence the obtained results hold for those indices; more precisely, one of the obtained results covers the recently developed elliptic Sombor and Zagreb-Sombor indices, while another result covers the recently introduced Euler-Sombor index.}
}