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 where denotes the degree of vertex in . 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.

Let G be a connected graph with vertex set V(G) and edge set E(G). The Sombor index of G is defined asRecent results of Sombor index can be found in References [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].A chemical tree is a tree with d v ≤ 4 for all v ∈ V(G). For details on chemical trees, see . Let T n (CT n ) be the set of trees (chemical trees) with n vertices. Let T n,k (CT n,k ) be the set of trees (chemical trees) with n vertices and k pendent vertices.

Hexagonal chains are a special class of catacondensed benzenoid system and phenylene chains are a class of polycyclic aromatic compounds. Recently, A family of Sombor indices was introduced by Gutman in the chemical graph theory. It had been examined that these indices may be successfully applied on modeling thermodynamic properties of compounds. In this paper, we study the expected values of the Sombor indices in random hexagonal chains, phenylene chains, and consider the Sombor indices of some chemical graphs such as graphene, coronoid systems and carbon nanocones.

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Topological indices are a class of numerical invariants that predict certain physical and chemical properties of molecules. Recently, a novel topological index, named as Sombor index, was introduced by Gutman, defined aswhere d u denotes the degree of vertex u.In this paper, our aim is to order the chemical trees, chemical unicyclic graphs, chemical bicyclic graphs and chemical tricyclic graphs with respect to their Sombor index. We find 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.