Abstract
For a (chemical) graph \(G\) with vertex set \(V_{G}\) and edge set \(E_{G}\), the Sombor index is defined as \(SO(G)=\sum\limits_{uv\in E_{G}}\sqrt{d^{2}(u)+d^{2}(v)}\), where \(d(u)\) denotes the degree of vertex \(u\) in \(G\). In this paper, we determine
the second and third minimum (resp. maximum) Sombor index of catacondensed hexagonal systems and phenylenes, the second minimum Sombor index of cata-catacondensed fluoranthene-type benzenoid systems. We also determine the minimum (resp.
maximum) Sombor index of caterpillar trees with given degree sequence. At last, the first three maximum and the minimum Sombor index of star-like trees are determined.