TY  - JOUR
AU  - Ali, Akbar
AU  - Dimitrov, Darko
AU  - Réti, Tamás
AU  - Alotaibi, Abdulaziz Mutlaq
AU  - Alanazi, Abdulaziz M.
AU  - Hassan, Taher S.
PY  - 2025
TI  - Degree-based graphical indices of    k-cyclic graphs
JO  - AIMS Mathematics
SP  - 13540
EP  - 13554
VL  - 10
IS  - 6
AB  - 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.
UR  - https://doi.org/10.3934/math.2025609
DO  - 10.3934/math.2025609