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Boron, the element which is in close proximity with carbon in the periodic table has been hypothesized to produce diverse two‐dimensional structures that differ from well‐studied 2D materials. Icosahedron B12$$ {\mathcal{B}}_{12} $$, the monomers of which form the crystalline boron structure, appears as a recurring pattern in the chemistry of boron compounds, elemental boron and boron‐rich materials, functions as a building block in a majority of boron allotropes. The topological study of the icosahedral sheets is a necessary field to be investigated for the effective analysis and characterization of its physico‐chemical attributes without undertaking time‐consuming experimental research. The topological descriptors being expressed as numerical values enable scientists to compare and correlate data, which can be applied to quantitative structure‐activity relationships and quantitative structure‐property relationships modeling. In this study, various degree based molecular descriptors of the crystal boron icosahedral α$$ \alpha $$ sheet Bα(a,b)$$ {\mathcal{B}}_{\alpha}\left(\mathfrak{a},\mathfrak{b}\right) $$ has been formulated from a two‐dimensional lattice perspective using the 필‐polynomial approach. To establish the significance of these descriptors in the study of chemical attributes, an efficient linear regression modeling has also been performed, enabling the prediction of properties of several other boron sheets. [ABSTRACT FROM AUTHOR]

Dendrimers are hyperbranched monodisperse macromolecules with constraint size and are shape persistent. Topological indices are numerical parameters that provide a correlation with the chemical, physical, and biological properties of the molecular structure. We have computed distance based molecular descriptors of polyphenylene dendrimer using the technique, quotient of quotient graphs, and analyzed a graphical comparison. This technique helps in obtaining numerical expressions of molecular descriptors on complex chemical structures. Our results help in better understanding of the properties of polyphenylene dendrimer which can be used in drug design. [ABSTRACT FROM AUTHOR]

Topological descriptors have drawn more interest recently because of the simplicity of generation and quick evaluation times, by avoiding time-consuming laboratory experiments. The distance based descriptors stand out as being pivotal in the QSAR and QSPR analysis of physico-chemical aspects. Dendrimers are branching polymeric molecules distinguished by its systematic growth pattern. Non-conjugated Ethylene oxide dendritic core attached with tetraphenylethylene is one such hyper branched polymer with strong solubility in a majority of organic solvents making them an active constituent for a variety of experimental purposes. No significant amount of research has been carried over based on the topological aspects of this dendrimer. This study effectively establishes the correlation between the chemical and physical attributes of the structure which can further aid in experimental research. In this work, various fundamental distance based descriptors of Ethylene oxide cored dendrimer have been evaluated by converting the original graph to quotient graphs using Djokovic̀-Winkler relation. Moreover, a graphical comparison of these descriptors has also been plotted to help comprehend the growth trend of these numerical values. [ABSTRACT FROM AUTHOR]

Macromolecules are gaining much attention in various fields today. Dendrimers are artificially synthesized macromolecules by convergent or divergent approach. They are compact regular structures with spherical dimension and has a vast number of application in disparate fields such as drug delivery, material science, and biology, magnetic resonance imaging, an organic light-emitting device, etc. Determining the pharmacological, chemical, and biological characteristics of a substance necessitates a significant amount of effort. From the chemical graph of the dendrimer structure, we can infer those characteristics with the help of numerical descriptors known as the topological index. The Wiener and Szeged indices are two important distance-based topological indices applicable in nanoscience. The degree-based topological indices also have great importance and huge applications in structural chemistry. These indices together with graph entropy are found to be more effective and have found application in different sciences. In this work, the Wiener index, Szeged indices, Mostar indices, and Padmakar Ivan index for cyclen cored dendrimers are evaluated by converting the original graph into quotient graphs using Θ * - classes. This technique is applied since the regular cut method is a lengthy process while moving on to higher generations and also due to the presence of odd cycles in the structure. The degree-based indices and the degree-based graph entropies for the cyclen cored dendrimers are further studied. The comparison graphs with respect to the topological indices as well as graph entropies are also presented. [ABSTRACT FROM AUTHOR]

Nanosheets with boron elements have excellent characteristics which makes the boron polymorphs unique and super hard. A boron α -icosahedral nanosheet in crystalline form has superconductivity and thermal electronic properties. In theoretical chemistry and QSPR/QSAR study, a topological descriptor is an important analytical tool. It helps to analyse the structure and its properties and also correlates the with numerical expressions. The valence-based M-polynomial provides quantitative measures of molecular properties based on their geometric, electrostatic, and quantum chemical characteristics. In this article, the QSPR/QSAR analysis is performed for this nanosheet and the analytical expressions are validated with original synthesized data, and received excellent correlation values of 0.9835 and 0.9932. The mathematical expression of the structure is analysed and the indices are compared graphically and numerically. [ABSTRACT FROM AUTHOR]

In the current era of technological advancement, dendrimers have been in high demand as the fundamental component in the field of drug design. For better efficacy, scientists have been working intensely to produce potentially beneficial dendrimer molecules. Mathematical chemistry has a lot to offer with effective tools like molecular descriptors and functions that can forecast compound molecular features. Topological descriptors, being numerical invariants associated with a chemical compound, have the potential to correlate chemical structure with different physical attributes, chemical reactivity, or biological activity. By incorporating these descriptors in QSAR and QSPR modeling, it is possible to predict a variety of physicochemical attributes and bioactivities. Hence, the main objective of the study is to obtain the distance‐based molecular descriptors of triazine‐based dendrimer and subsequently generate linear models for their chemical properties using regression analysis. This linear model can predict the properties of succeeding generations, avoiding the necessity for time‐consuming laboratory experimental trials. [ABSTRACT FROM AUTHOR]

The role of dendrimers is getting updated and grabbing immense attention in many fields. Dendrimers are used in a broad spectrum, in specific, it is widely utilized in drug delivery, for targeted carrier and specific action. Also, in drug catalysis, it improves the solubility of poorly soluble drugs and increases the stability of active ingredients within the cores. Many researchers are interested in developing new dendrimers by using various compounds. π‐conjugated dendrimers via truxenes and thienylethynylene units, are considered a promising material in the field of medicinal chemistry, bio‐organic, and environmental sciences. In QSAR/QSPR, the structural analysis of chemical compounds is examined by topological descriptors. In this article, the various distance‐based topological indices such as Wiener, Szeged, and Mostar of gradient star‐persistent π‐conjugated dendrimers are determined. Since gradient star‐persistent π‐conjugated dendrimers have odd cycles, the usual cut method is not applicable, therefore we use a new concept, the quotient of quotient graph to determine the numerical expression of various indices. An analysis of linear regression reveals that degree‐based topological descriptors predict better physicochemical properties. [ABSTRACT FROM AUTHOR]

The molecular descriptors are numerical quantities which provide information and characteristics of chemical structures. The molecular descriptors provides characteristics such as boiling point, solubility, toxicity, melting point, vapor pressure, etc. Dendrimers are hyperbranched macromolecules with constraint size which plays a major role in the field of medicine especially nanomedicine. In this paper, we have derived distance-based topological indices, namely, Wiener, Szeged, Mostar, and Padmakar Ivan index of porphyrin dendrimer. Also, a graphical comparison among the distance-based topological indices of porphyrin dendrimer has been provided. [ABSTRACT FROM AUTHOR]