Extremal cacti with respect to Sombor index

Abstract

Recently, a novel topological index, Sombor index, was introduced by Gutman, defined as $SO(G)=\sum _{uv\in E(G)}\sqrt{d_u^2+d_v^2}$, where $d_u$ denotes the degree of vertex $u$. In this paper, we first determine the maximum Sombor index among cacti with $n$ vertices and $t$ cycles, then determine the maximum Sombor index among cacti with perfect matchings. We also characterize corresponding maximum cacti.

arXiv comment14 pages, 1 figure