HDR Degree Bassed Indices and Mhr-Polynomial for the Treatment of COVID-19

In this research work, We introduce topological indices, namely as an HDR version of Modified Zagreb topological index (HDRM*), HDR version of Modified forgotten topological index (HDRF*), and HDR version of hyper Zagreb index (HDRHM*). Then the relatively study depends on the structure-property regression analysis to test and compute the chemical applicability of these indices to predict the physicochemical properties of octane isomers. Also, we show these HDR indices have well degeneracy properties compared to other degree-based topological indices. Also, We defined and computed the Mhr-polynomial of the newly indices and applied it on COVID-19 treatments. Also, we discussed some mathematical properties of HDR indices.

Novel Degree-Based Topological Descriptors of Carbon Nanotubes

The most significant tool of mathematical chemistry is the numerical descriptor called topological index. Topological indices are extensively used in modelling of chemical compounds to analyse the studies on quantitative structure activity/property/toxicity relationships and combinatorial library virtual screening. In this work, an attempt is made in defining three novel descriptors, namely, neighborhood geometric-harmonic, harmonic-geometric, and neighborhood harmonic-geometric indices. Also, the aforementioned three indices along with the geometric-harmonic index are tested for physicochemical properties of octane isomers using linear regression models and computed for some carbon nanotubes.

Sharp Bounds for the Inverse Sum Indeg Index of Graph Operations

Vukičević and Gasperov introduced the concept of 148 discrete Adriatic indices in 2010. These indices showed good predictive properties against the testing sets of the International Academy of Mathematical Chemistry. Among these indices, twenty indices were taken as beneficial predictors of physicochemical properties. The inverse sum indeg index denoted by ISI G k of G k is a notable predictor of total surface area for octane isomers and is presented as ISI G k = ∑ g k g k ′ ∈ E G k d G k g k d G k g k ′ / d G k g k + d G k g k ′ , where d G k g k represents the degree of g k ∈ V G k . In this paper, we determine sharp bounds for ISI index of graph operations, including the Cartesian product, tensor product, strong product, composition, disjunction, symmetric difference, corona product, Indu–Bala product, union of graphs, double graph, and strong double graph.

Physicochemical Properties of Octane Isomers in View of the Structural Numbers

The structural features of octane isomers were quantified with help of the Structural Numbers. A Mutually Optimized Contribution of the Structural Numbers (MOCSN) was used to calculate which parts of information regarding branching contribute the tested Structural Numbers. Besides the known Structural Numbers, two Asymmetry Numbers were developed in order to quantify the asymmetry of the octane isomers, one regarding the asymmetry along the main chain of the molecule and the other one regarding the asymmetry perpendicular to the main chain of the molecule. Their correlation to the values of 29 tested physicochemical properties of octanes was low, |R| < 0.6. After optimization of the Mutually Optimized Contribution of the Structural Numbers, the Information Content of the Mutually Optimized Contribution of the Structural Numbers ranged from 34.3% to 89.0% of the information contained in the physicochemical properties. The Structural Numbers enable the first step of the structural interpretation of physicochemical properties of octane isomers. In 17 out of 29 cases the most of information contained in the physicochemical properties is presented among the Structural Numbers by the Number of Branches, in 8 cases by the Peripheral Number, in 3 cases by an Asymmetry Number and in 1 case by the Distance Number.

Generalized Reciprocal Sanskruti Index: Chemical Applicability and Bounds

In this paper, we put forward the generalization of reciprocal Sanskruti index RS^α for some α∈Z^+. For α=3 the prediction potentiality of RS^3 is discussed with the physicochemical properties of the set of octane isomers. And also we study the mathematical properties of RS^3.

Computing Analysis of Connection-Based Indices and Coindices for Product of Molecular Networks

Gutman and Trinajstić (1972) defined the connection-number based Zagreb indices, where connection number is degree of a vertex at distance two, in order to find the electron energy of alternant hydrocarbons. These indices remain symmetric for the isomorphic (molecular) networks. For the prediction of physicochemical and symmetrical properties of octane isomers, these indices are restudied in 2018. In this paper, first and second Zagreb connection coindices are defined and obtained in the form of upper bounds for the resultant networks in the terms of different indices of their factor networks, where resultant networks are obtained from two networks by the product-related operations, such as cartesian, corona, and lexicographic. For the molecular networks linear polynomial chain, carbon nanotube, alkane, cycloalkane, fence, and closed fence, first and second Zagreb connection coindices are computed in the consequence of the obtained results. An analysis of Zagreb connection indices and coindices on the aforesaid molecular networks is also included with the help of their numerical values and graphical presentations that shows the symmetric behaviour of these indices and coindices with in certain intervals of order and size of the under study (molecular) networks.