Search Results (6)

The structure and topology of chemical compounds can be determined using chemical graph theory. Using topological indices, we may uncover much about connectivity, complexity, and other important aspects of molecules. Numerous research investigations have been conducted on the K-Banhatti indices and entropy measurements in various fields, including the study of natural polymers, nanotubes, and catalysts. At the same time, the Shannon entropy of a graph is widely used in network science. It is employed in evaluating several networks, including social networks, neural networks, and transportation systems. The Shannon entropy enables the analysis of a network’s topology and structure, facilitating the identification of significant nodes or structures that substantially impact network operation and stability. In the past decade, there has been a considerable focus on investigating a range of nanostructures, such as nanosheets and nanoparticles, in both experimental and theoretical domains. As a very effective catalyst and inert substrate, the $MgO$ nanostructure has received a lot of interest. The primary objective of this research is to study different indices and employ them to look at entropy measures of magnesium oxide(111) nanosheets over a wide range of p values, including $p=1,2,3,\dots ,j$. Additionally, we conducted a linear regression analysis to establish the correlation between indices and entropies. Full article

Entropy is a thermodynamic function used in chemistry to determine the disorder and irregularities of molecules in a specific system or process. It does this by calculating the possible configurations for each molecule. It is applicable to numerous issues in biology, inorganic and organic chemistry, and other relevant fields. Metal–organic frameworks (MOFs) are a family of molecules that have piqued the curiosity of scientists in recent years. They are extensively researched due to their prospective applications and the increasing amount of information about them. Scientists are constantly discovering novel MOFs, which results in an increasing number of representations every year. Furthermore, new applications for MOFs continue to arise, illustrating the materials’ adaptability. This article investigates the characterisation of the metal–organic framework of iron(III) tetra-p-tolyl porphyrin (FeTPyP) and CoBHT (CO) lattice. By constructing these structures with degree-based indices such as the K-Banhatti, redefined Zagreb, and the atom-bond sum connectivity indices, we also employ the information function to compute entropies. Full article

The cloud computing networks used in the IoT, and other themes of network architectures, can be investigated and improved by cheminformatics, which is a combination of chemistry, computer science, and mathematics. Cheminformatics involves graph theory and its tools. Any number that can be uniquely calculated by a graph is known as a graph invariant. In graph theory, networks are converted into graphs with workstations or routers or nodes as vertex and paths, or connections as edges. Many topological indices have been developed for the determination of the physical properties of networks involved in cloud computing. The study computed newly prepared topological invariants, K-Banhatti Sombor invariants (KBSO), Dharwad invariants, Quadratic-Contraharmonic invariants (QCI), and their reduced forms with other forms of cloud computing networks. These are used to explore and enhance their characteristics, such as scalability, efficiency, higher throughput, reduced latency, and best-fit topology. These attributes depend on the topology of the cloud, where different nodes, paths, and clouds are to be attached to achieve the best of the attributes mentioned before. The study only deals with a single parameter, which is a topology of the cloud network. The improvement of the topology improves the other characteristics as well, which is the main objective of this study. Its prime objective is to develop formulas so that it can check the topology and performance of certain cloud networks without doing or performing experiments, and also before developing them. The calculated results are valuable and helpful in understanding the deep physical behavior of the cloud’s networks. These results will also be useful for researchers to understand how these networks can be constructed and improved with different physical characteristics for enhanced versions. Full article

Entropy is a measure of a system’s molecular disorder or unpredictability since work is produced by organized molecular motion. Shannon’s entropy metric is applied to represent a random graph’s variability. Entropy is a thermodynamic function in physics that, based on the variety of possible configurations for molecules to take, describes the randomness and disorder of molecules in a given system or process. Numerous issues in the fields of mathematics, biology, chemical graph theory, organic and inorganic chemistry, and other disciplines are resolved using distance-based entropy. These applications cover quantifying molecules’ chemical and electrical structures, signal processing, structural investigations on crystals, and molecular ensembles. In this paper, we look at K-Banhatti entropies using K-Banhatti indices for $C_6{H}_6$ embedded in different chemical networks. Our goal is to investigate the valency-based molecular invariants and K-Banhatti entropies for three chemical networks: the circumnaphthalene ($CN{B}_n$), the honeycomb ($H{B}_n$), and the pyrene ($P{Y}_n$). In order to reach conclusions, we apply the method of atom-bond partitioning based on valences, which is an application of spectral graph theory. We obtain the precise values of the first K-Banhatti entropy, the second K-Banhatti entropy, the first hyper K-Banhatti entropy, and the second hyper K-Banhatti entropy for the three chemical networks in the main results and conclusion. Full article

Entropy is a thermodynamic function in physics that measures the randomness and disorder of molecules in a particular system or process based on the diversity of configurations that molecules might take. Distance-based entropy is used to address a wide range of problems in the domains of mathematics, biology, chemical graph theory, organic and inorganic chemistry, and other disciplines. We explain the basic applications of distance-based entropy to chemical phenomena. These applications include signal processing, structural studies on crystals, molecular ensembles, and quantifying the chemical and electrical structures of molecules. In this study, we examine the characterisation of polyphenylenes and boron ($B_{12}$) using a line of symmetry. Our ability to quickly ascertain the valences of each atom, and the total number of atom bonds is made possible by the symmetrical chemical structures of polyphenylenes and boron $B_{12}$. By constructing these structures with degree-based indices, namely the K Banhatti indices, $ReZ{G}_1$-index, $ReZ{G}_2$-index, and $ReZ{G}_3$-index, we are able to determine their respective entropies. Full article

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. Full article