A note on Sombor indices of cacti

Abstract

The Sombor index is a novel degree based topological index, based on geometrical
considerations. For a graph $G$, the Sombor index is defined as the sum over
all edges $uv$ of $G$ of the terms $\sqrt{d_u^2+d_v^2}$
where $d_u,d_v$ denote the degrees of the end vertices of $uv$.
In this paper, we determine the first two species with maximum Sombor and exponential Sombor indices
among cacti of a fixed order and fixed number of cycles. We also characterize such extremal cacti
for reduced Sombor index, average Sombor index and $p$-Sombor index, as well as
for generalized Sombor index. By this we extend the results by Das \cite{das2024open}
and Liu \cite{liu2021extremal}.