Abstract
Topological indices are a class of numerical invariants that
predict certain physical and chemical properties of molecules.
Recently, two novel topological indices, named as Sombor index
and reduced Sombor index, were introduced by Gutman, defined as
\[
SO(G) = \sum_{uv\in E(G)} \sqrt{d_G^2(u) + d_G^2(v)}\,,
\]
\[
SO(G) = \sum_{uv\in E(G)} \sqrt{(d_G(u) - 1)^2 + (d_G(v) - 1)^2}\,,
\]
where \(d_G(u)\) denotes the degree of vertex \(u\) in \(G\). In
this paper, our aim is to order the chemical trees, chemical
unicyclic graphs, chemical bicyclic graphs and chemical tricyclic
graphs with respect to Sombor index and reduced Sombor index.
We determine the first fourteen minimum chemical trees, the first
four minimum chemical unicyclic graphs, the first three minimum
chemical bicyclic graphs, the first seven minimum chemical
tricyclic graphs. At last, we consider the applications of reduced
Sombor index to octane isomers.
