Structure-property modeling of coumarins and coumarin-related compounds in pharmacotherapy of cancer by employing graphical topological indices.

Coumarins, a subgroup of colorless and crystalline oxygenated heterocyclic compounds originally discovered in the plant Dipteryx odorata, were the subject of a recent study investigating their quantitative structure-activity relationship (QSAR) in cancer pharmacotherapy. This study utilized graph theoretical molecular descriptors, also known as topological indices, as a numerical representation method for the chemical structures embedded in molecular graphs. These descriptors, derived from molecular graphs, play a pivotal role in quantitative structure-property relationship (QSPR) analysis. In this paper, intercorrelation between the Balban index, connective eccentric index, eccentricity connectivity index, harmonic index, hyper Zagreb index, first path Zagreb index, second path Zagreb index, Randic index, sum connectivity index, graph energy and Laplacian energy is studied on the set of molecular graphs of coumarins. It is found that the pairs of degree-based indices are highly intercorrelated. The use of these molecular descriptors in structure-boiling point modeling was analyzed. Finally, the curve-linear regression between considered molecular descriptors with physicochemical properties of coumarins and coumarin-related compounds is obtained.

Locating-dominating number of certain infinite families of convex polytopes with applications.

A convex hull of finitely many points in the Euclidean space Rd is known as a convex polytope. Graphically, they are planar graphs i.e. embeddable on R2. Minimum dominating sets possess diverse applications in computer science and engineering. Locating-dominating sets are a natural extension of dominating sets. Studying minimizing locating-dominating sets of convex polytopes reveal interesting distance-dominating related topological properties of these geometrical planar graphs. In this paper, exact value of the locating-dominating number is shown for one infinite family of convex polytopes. Moreover, tight upper bounds on γl-d are shown for two more infinite families. Tightness in the upper bounds is shown by employing an updated integer linear programming (ILP) model for the locating-dominating number γl-d of a fixed graph. Results are explained with help of some examples. The second part of the paper solves an open problem in Khan (2023) [28] which asks to find a domination-related parameter which delivers a correlation coefficient of ρ>0.9967 with the total π-electronic energy of lower benzenoid hydrocarbons. We show that the locating-dominating number γl-d delivers such a strong prediction potential. The paper is concluded with putting forward some open problems in this area.

Graphs with given connectivity and their minimum Sombor index having applications to QSPR studies of monocarboxylic acids.

The Sombor index, introduced by Gutman in 2021, represents a novel graphical topological descriptor reliant upon graph degree information. It holds promise for elucidating the thermodynamic behavior of compounds. Denoting by Vnk (respectively, Enk) the set encompassing all connected graphs comprising n vertices with a specific vertex-connectivity (correspondingly, edge-connectivity) value of k. In Problem 1 (resp. Problem 2) of Hayat et al. (2022) [33], the question of finding minimum Sombor index of graphs in Vnk (resp. Enk) is proposed. In this note, we solve both of the open problems by characterizing minimizing graphs in Enk and Vnk corresponding to the Sombor index. We employed commonly occurring valency-based graphical indices in a QSPR studies of the physicochemical characteristics for monocarboxylic acids. The proposed statistical models infer that the Sombor index predicts various physicochemical characteristics for monocarboxylic acids having strong predictive coefficients such as ρ=0.99998.