Recently a novel class of degree-based topological molecular descriptors was proposed, the so-called Sombor indices. Within this study, the predictive and discriminative potentials of Sombor index, reduced Sombor index, and average Sombor index were examined. All three topological molecular descriptors showed good predictive potential. Statistical data indicate that the reduced Sombor index preforms with slightly better predictive potential. An external validation confirms this finding. It was found that these degree-based indices exert modest discriminative potential, when tested on a large group of isomers.

The energy of graphs containing self-loops is considered. If the graph G of order n contains σ self-loops, then its energy is defined as E(G) = |λ i − σ/n| where λ 1 , λ 2 , . . . , λ n are the eigenvalues of the adjacency matrix of G. Some basic properties of E(G) are established, and several open problems pointed out or conjectured.

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The relationship between the resolvent and Estrada indices for the alkanes has been recently demonstrated. That relationship involved the first Zagreb index besides these two eigenvalue-based molecular descriptors. In this paper, the quality of the correlation is tested in the case of isomeric benzenoid hydrocarbons, where the first Zagreb index is constant. Extraordinary linear correlations are identified for all studied groups of isomeric benzenoid hydrocarbons. Additionally, the relationship of these indices with the boiling points of a set of benzenoid hydrocarbons is presented.

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Three eigenvalue-based topological molecular descriptors are compared using several datasets of alkanes. Two of them are well-known and frequently employed in various QSPR/QSAR investigations, and third-one is a newly derived whose predictive potential is yet to be proven. The relations among them are found and discussed. Structural parameters that govern these relations are identified and the corresponding formulas based on multiple linear regression have been obtained. It has been shown that all three investigated indices are encoding almost the same structural information of a molecule. They differ only by the extent of the sensitivity on a structural branching of a molecule and on the number of non-bonding molecular orbitals.

The paper is concerned with the Sombor index (SO) of Kragujevac trees (Kg). A slightly more general definition of Kg is offered. SO is a recently introduced degree-based topological index. A general combinatorial expression for SO(Kg) is established. The species with minimum and maximum SO(Kg)-values are determined.