University of KashanIranian Journal of Mathematical Chemistry2228-648912420211201Extremal Cacti with respect to Sombor index19720811163210.22052/ijmc.2021.243026.1582ENHechaoLiuSchool of Mathematical Sciences, South China Normal University, Guangzhou, 510631, P. R. China0000-0001-7606-4842Journal Article20210821Recently, a novel topological index, Sombor index, was introduced by Gutman, defined as $SO(G)=\sum\limits_{uv\in E(G)}\sqrt{d_{u}^{2}+d_{v}^{2}}$, 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.https://ijmc.kashanu.ac.ir/article_111632_de6f31ed2e636e86763d50333fb73e29.pdf