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Dendrimers are well-defined nanoparticles, which have far-reaching application in the field of chemistry. Many efforts have been devoted to development of dendrimer due to thier unique structure and various properties and broad application. It helps in varieties of purposes as a catalyst in drug delivery and drug design. The topological descriptor analyze the structure–property relationship of chemical compounds. In this paper, some numerical expressions have been obtained to understand the behavioral pattern of chiral polyamidoamine (PAMAM) dendrimer and PAMAM anthracene moieties dendrimer. The analytical expression has been plotted and compared with varieties of indices to show how it varies between each indices.

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Measures of graph entropy have been widely used in information theory, biology, chemistry, and sociology, among other disciplines. The entropy of a probability distribution may be thought of as both an indicator of information and an indicator of uncertainty, and it is a number used in information theory to gauge the complexity of a graph. Mathematical and medicinal chemistry, including drug design, have previously made extensive use of information-theoretic network complexity measurements. Dendrimers belong to the world of molecular chemistry for stepwise controlled synthesis and to the world of polymers for repeating structures from monomers. A topological index is a numerical metric that describes the topology of a graph. Consequently , a topological index calculated for a molecular network is a quantitative indicator of molecular topology. Due to the simplicity of production and the speed at which these computations may be performed, these descriptors have gained great prominence in recent years. Characterizing molecular structure using topological methods, including numerical graph invariants, is a current trend in mathematics and computational chemistry. Such conceptual descriptors have also launched a broad range of applications in QSAR/QSPR investigations and is ideal for innovative molecular design, drug development, and risk assessment of chemicals. In this paper, various entropy measures along with the distance and degree based topological indices of highly efficient iridium cored electrophosphorescent dendrimer has been evaluated. Entropy measure is a topological feature that may be used to assess the complexity of chemical compounds.

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In this article, a novel technique to evaluate and compare the neighborhood degree molecular descriptors of two variations of the carbon nanosheet C5C7(a,b) is presented. The conjugated molecules follow the graph spectral theory, in terms of bonding, non-bonding and antibonding Ruckel molecular orbitals. They are demonstrated to be immediately determinable from their topological characteristics. The effort of chemical and pharmaceutical researchers is significantly increased by the need to conduct numerous chemical experiments to ascertain the chemical characteristics of such a wide variety of novel chemicals. In order to generate novel cellular imaging techniques and to accomplish the regulation of certain cellular mechanisms, scientists have utilized the attributes of nanosheets such as their flexibility and simplicity of modification, out of which carbon nanosheets stand out for their remarkable strength, chemical stability, and electrical conductivity. With efficient tools like polynomials and functions that can forecast compound features, mathematical chemistry has a lot to offer. One such approach is the M-polynomial, a fundamental polynomial that can generate a significant number of degree-based topological indices. Among them, the neighborhood M-polynomial is useful in retrieving neighborhood degree sum-based topological indices that can help in carrying out physical, chemical, and biological experiments. This paper formulates the unique M-polynomial approach which is used to derive and compare a variety of neighborhood degree-based molecular descriptors and the corresponding entropy measures of two variations of pent-heptagonal carbon nanosheets. Furthermore, a regression analysis on these descriptors has also been carried out which can further help in the prediction of various properties of the molecule.

Carbon nanoparticles are gaining much importance in the contemporary world. Among which carbon nanocones have wide range of acceptance in the field of nanotechnology due to its effective properties and applications. Nanocones, also known as nanohorns are carbon networks which are planar in structure and has majority of hexagonal faces along with some non-hexagonal faces, which are most commonly pentagons. Nanocones which include pentagons in their structure can be referred to as adjacently or non-adjacently configured pentagonal structure of nanocones. Carbon nanocones possess properties like specific surface area, high yield, high chemical stability, high purity, low toxicities, exceptional catalytic properties, superior porosity, and good conductivity compared to other carbon nanostructures. These exceptional properties help nanocones to be a good replacement for carbon nanotube. Also nanocones have secured its place in fields like electrochemical sensing or biosensing, biofuel cell, as an electrode material, supercapacitor, gas storage device and biomedical applications. The information entropy was introduced to analyse and quantify the complexity of data and information transmission. It is applied to study the complexity and the quantum chemical electron densities of molecular structures. Later, the idea of graph entropy came into role to characterise the complexity of graphs. The concept of graph entropy is to assign a probablity function to the edges in the chemical graph using the topological descriptor. In this work, the degree based descriptors and the corresponding graph entropies for the adjacently and non-adjacently configured pentagonal structure of nanocones are determined.