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.
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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