On entropy measures of molecular graphs using topological indices

Graph theoretical descriptors differentiate d-Mannose isomers in the principal component proposed feature space: A computational approach

The intricate nature of carbohydrates, particularly monosaccharides, stems from the existence of several chiral centers within their tertiary structures. Predicting and characterizing the molecular geometries and electrostatic landscapes of these substances is difficult due to their complex electrical properties. Moreover, these structures can display a substantial degree of conformational flexibility due to the presence of many rotatable bonds. Moreover, identifying and distinguishing between D and L enantiomers of monosaccharides presents a significant analytical obstacle since there is a need for empirically measurable properties that can distinguish them. This work uses Principal Component Analysis (PCA) to explore the chemical information included in 3D descriptors in order to comprehend the conformational space of d-Mannose stereoisomers. The isomers may be discriminated by utilizing 3D matrix-based indices, geometrical descriptors, and RDF descriptors. The isomers can be distinguished by descriptors, such as the Harary-like index from the reciprocal squared geometrical matrix (H_RG), Harary-like index from Coulomb matrix (H_Coulomb), Wiener-like index from Coulomb matrix (Wi_Coulomb), Wiener-like index from geometrical matrix (Wi_G), Graph energy from Coulomb matrix (SpAbs_Coulomb), Spectral absolute deviation from Coulomb matrix (SpAD_Coulomb), and Spectral positive sum from Coulomb matrix (SpPos_Coulomb). Among these descriptors, the first two, H_RG and H_Coulomb, perform the best in differentiation among the 3D-Matrix-Based Descriptors (3D-MBD) class. The results obtained from this study provide a significant chemical insight into the structural characteristics of the compounds inside the graph theoretical framework. These findings are likely to serve as the basis for developing new methods for analytical experiments.

Topological Entropy Characterization, NMR and ESR Spectral Patterns of Coronene-Based Transition Metal Organic Frameworks

Metal organic frameworks (MOFs) are topical crystalline materials with high porosity and inner surface areas synthesized from naturally occurring minerals. Such MOFs with transition metals have attracted considerable attention because of their fascinating morphological diversity and tunable characteristics. The coronene-based structural frameworks with transition metal atoms are synthesized by repeating a fixed coronene unit at several levels. In this study, topological indices and NMR and ESR spectral patterns are computed for these MOFs to shed light on their structures and spectral properties. We obtained mathematical expressions of topological indices based on degree and degree-sum values of MOFs for the rectangular, hexagonal, and parallelogram peripheral shapes. Furthermore, the entropy measures of these novel frameworks are evaluated with the help of index functionals and compared to a wide range of degree-based descriptors. The NMR and ESR spectral patterns have been obtained from the distance degree vector sequences and symmetries for the three MOFs.

A Paradigmatic Approach to Find the Valency-Based K-Banhatti and Redefined Zagreb Entropy for Niobium Oxide and a Metal-Organic Framework

Entropy is a thermodynamic function in chemistry that reflects the randomness and disorder of molecules in a particular system or process based on the number of alternative configurations accessible to them. Distance-based entropy is used to solve a variety of difficulties in biology, chemical graph theory, organic and inorganic chemistry, and other fields. In this article, the characterization of the crystal structure of niobium oxide and a metal-organic framework is investigated. We also use the information function to compute entropies by building these structures with degree-based indices including the K-Banhatti indices, the first redefined Zagreb index, the second redefined Zagreb index, the third redefined Zagreb index, and the atom-bond sum connectivity index.

Computing the Entropy Measures for the Line Graphs of Some Chemical Networks

Chemical Graph entropy plays a significant role to measure the complexity of chemical structures. It has explicit chemical uses in chemistry, biology, and information sciences. A molecular structure of a compound consists of many atoms. Especially, the hydrocarbons is a chemical compound that consists of carbon and hydrogen atoms. In this article, we discussed the concept of subdivision of chemical graphs and their corresponding line chemical graphs. More preciously, we discuss the properties of chemical graph entropies and then constructed the chemical structures namely triangular benzenoid, hexagonal parallelogram, and zigzag edge coronoid fused with starphene. Also, we estimated the degree-based entropies with the help of line graphs of the subdivision of above mentioned chemical graphs.

On physical analysis of topological indices via curve fitting for natural polymer of cellulose network

Plant materials are processed in a variety of ways to produce biologically active compounds. Cellulose (natural polymer) has the ability to deliver physiologically active compounds to organ targets that have been extracted by CO 2 . Researchers have recently become interested in polymers that can transport biologically active compounds into human bodies. For appropriately selecting bearers of biologically active chemicals, knowledge of the thermodynamic properties of cellulose is required. In QSPR/QSAR modelling, which provides the theoretical and optimum foundation for costly experimental drug discovery, molecular descriptors are extremely important. In this article, we investigated a natural polymer of cellulose network which has interesting pharmacological applications, outstanding characteristics, and a novel molecular structure. We plan to look into and compute a variety of closed-form formulas of various K-Banhatti indices along with their respective K-Banhatti entropies and the heat of formation. The numerical and graphical characterization of computed results was combined with curve fitting between calculated thermodynamic properties and topological indices. This presentation will provide a complete description of potentially important thermodynamic features that could be useful in modifying the structure of natural polymer of cellulose network CN y x .

Real-World Data Difficulty Estimation with the Use of Entropy

In the era of the Internet of Things and big data, we are faced with the management of a flood of information. The complexity and amount of data presented to the decision-maker are enormous, and existing methods often fail to derive nonredundant information quickly. Thus, the selection of the most satisfactory set of solutions is often a struggle. This article investigates the possibilities of using the entropy measure as an indicator of data difficulty. To do so, we focus on real-world data covering various fields related to markets (the real estate market and financial markets), sports data, fake news data, and more. The problem is twofold: First, since we deal with unprocessed, inconsistent data, it is necessary to perform additional preprocessing. Therefore, the second step of our research is using the entropy-based measure to capture the nonredundant, noncorrelated core information from the data. Research is conducted using well-known algorithms from the classification domain to investigate the quality of solutions derived based on initial preprocessing and the information indicated by the entropy measure. Eventually, the best 25% (in the sense of entropy measure) attributes are selected to perform the whole classification procedure once again, and the results are compared.

Topological Characterization and Graph Entropies of Tessellations of Kekulene Structures: Existence of Isentropic Structures and Applications to Thermochemistry, Nuclear Magnetic Resonance, and Electron Spin Resonance

Tessellations of kekulenes and cycloarenes are of considerable interest as nanomolecular belts in trapping and transportation of heavy metal ions and chloride ions, as they possess optimal electronic features and pore sizes. A class of cycloarenes called kekulenes have been the focus of several experimental and theoretical studies from the stand point of aromaticity, superaromaticity, chirality, and novel electrical and magnetic properties. In the present study, we investigate the entropies and topological characterization of different tessellations of kekulenes through topological computations of superaromatic structures with pores. We introduce the self-powered vertex degree-based topological indices and then derive the graph entropy measures for three different tessellations (zigzag, armchair, and rectangular) via various molecular descriptors that we derive here. Several applications to computing the molecular properties are pointed out. We demonstrate the existence of isentropic and yet nonisomorphic tessellations of kekulenes for the first time. The two tessellations are predicted to be quite close in energy with comparable energy gaps. Graph theory-based PPP methods with parameters derived from higher levels of theory are proposed to be promising tools for the predictions of relative stabilities of kekulene tessellations. We show that the developed techniques can be applied in the general context of artificial intelligence for the machine generation of nuclear magnetic resonance and electron spin resonance spectroscopic patterns as well as in robust computations of thermochemistry of a large combinatorial libraries of tessellations of kekulenes through the generation of bond-equivalence classes.

On eccentricity-based entropy measures for dendrimers

The eccentricity-based entropy inspired by Shannon's entropy approach is the information-theoretic quantity to figure out the structural information of complex networks. The investigation for advance biomedical utilization of dendrimers has improved the synthesis of radical based molecules. Categorically, attaining radical dendrimers has initiated their use in different fields such as anti-tumor agents and as magnetic resonance imaging. The use of radical dendrimers has increased the possibility of establishing new kinds of devices based on para-magnetic axioms of organic radicals. In this article, we discussed dendrimer based on cyclotriphosphazene ( N 3 P 3 ) which has balanced edge groups and these are examined by EPR temperature spectrum. Firstly, we computed eccentricity-based indices and then we computed eccentricity based entropies by developing an acquaintance between these indices and their entropies. Moreover we presented our computed result numerically and graphically which leads to good importance of our contribution.

On Knowledge Discovery and Representations of Molecular Structures Using Topological Indices

The main purpose of a topological index is to encode a chemical structure by a number. A topological index is a graph invariant, which decribes the topology of the graph and remains constant under a graph automorphism. Topological indices play a wide role in the study of QSAR (quantitative structure-activity relationship) and QSPR (quantitative structure-property relationship). Topological indices are implemented to judge the bioactivity of chemical compounds. In this article, we compute the ABC (atom-bond connectivity); ABC 4 (fourth version of ABC), GA (geometric arithmetic) and GA 5 (fifth version of GA) indices of some networks sheet. These networks include: octonano window sheet; equilateral triangular tetra sheet; rectangular sheet; and rectangular tetra sheet networks.