Search

Polyphenyls and their derivatives, which are used in heat exchangers, drug synthesis, organic synthesis, and so on, have attracted the attention of researchers in various fields for many years. In this paper, we determine the expected values of the augmented Zagreb and arithmetic-geometric indices for this class of conjugated hydrocarbons. The comparisons between the expected values of these indices concerning the random polyphenyl chains have been determined explicitly. The graphical illustrations have been given in terms of the differences between the expected values of these indices. [ABSTRACT FROM AUTHOR]

Benzene is aromatic organic compound having six membered ring. Molecular studies provide evidence of presence of three alternative double bond providing exceptional stability to the molecule. Being basic unit of organic chemicals, benzene is widely used in pharmaceuticals, rubber, pesticides, dyes, lubricants, explosives and additives. Benzene derivatives are used in production of dyes, deodorants, pesticides, organic solvents, dispersants, plasticizers, and drugs. Keeping in view the extensive applications of benzene derivatives, we made use of QSPR analysis for predicting the multiple chemical and physical properties of organic compounds. By using SPSS software, correlation between newly introduced entropies and the Physico-chemical properties of benzene derivatives is examined. Our acquired consequences demonstrated that two physical properties of chemical structures, ie Boiling Point and enthalpy can be best predicted from the fifth ND entropy, and the other two properties namely Pie-electron Energy and molecular weight predicted from the neighborhood version of redefined first Zagreb entropy and neighborhood version of redefined second Zagreb entropy, respectively. [ABSTRACT FROM AUTHOR]

A topological index as a graph parameter was obtained mathematically from the graph's topological structure. These indices are useful for measuring the various chemical characteristics of chemical compounds in the chemical graph theory. The number of atoms that surround an atom in the molecular structure of a chemical compound determines its valency. A significant number of valency-based molecular invariants have been proposed, which connect various physicochemical aspects of chemical compounds, such as vapour pressure, stability, elastic energy, and numerous others. Molecules are linked with numerical values in a molecular network, and topological indices are a term for these values. In theoretical chemistry, topological indices are frequently used to simulate the physicochemical characteristics of chemical molecules. Zagreb indices are commonly employed by mathematicians to determine the strain energy, melting point, boiling temperature, distortion, and stability of a chemical compound. The purpose of this study is to look at valency-based molecular invariants for S i O 4 embedded in a silicate chain under various conditions. To obtain the outcomes, the approach of atom–bond partitioning according to atom valences was applied by using the application of spectral graph theory, and we obtained different tables of atom—bond partitions of S i O 4 . We obtained exact values of valency-based molecular invariants, notably the first Zagreb, the second Zagreb, the hyper-Zagreb, the modified Zagreb, the enhanced Zagreb, and the redefined Zagreb (first, second, and third). We also provide a graphical depiction of the results that explains the reliance of topological indices on the specified polynomial structure parameters. [ABSTRACT FROM AUTHOR]

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, R e Z G 1 -index, R e Z G 2 -index, and R e Z G 3 -index, we are able to determine their respective entropies. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Let G be a graph with n vertices and d i is the degree of its i th vertex ( d i is the degree of v i ), then the Zagreb matrix of G is the square matrix of order n whose (i , j) entry is equal to d i + d j if the i th and j th vertex of G are adjacent, and zero otherwise. The Zagreb energy Z E (G) of a graph G is defined as the sum of the absolute values of the eigenvalues of the Zagreb matrix. In this paper, we compute the Zagreb energy for some of the specific graphs, edge deleted graphs and complements graphs. Moreover, some properties of the eigenvalues and bounds for Zagreb energy are also discussed. [ABSTRACT FROM AUTHOR]

Corona virus cause diseases ranging from the common cold to Severe Acute Respiratory Syndrome (SARS). Several therapeutic agents have been evaluated for the treatment of Covid-19, but none have yet been shown to be efficacious. Remdesivir Gilead Sciences number (GS-5734), an inhibitor of the viral RNA-dependent, RNA polymerase with inhibitory activity against SARS-CoV and the Middle East respiratory syndrome (MERS-CoV), was identified early as a promising therapeutic candidate for Covid-19 because of its ability to inhibit SARS-CoV-2 invitro. Knowledge about the potential efficacy of Remdesivir against corona viruses has been restricted to in vitro studies and animal models. However, information related to COVID-19 is rapidly growing. Several clinical trials are ongoing for the management of COVID-19 using Remdesivir. Efficacy of Remdesivir (GS-5734) against Ebola virus has been demonstrated. In the field of Medical Science, concerning the definition of the topological index on the molecular structure and corresponding medical, biological, chemical, pharmaceutical properties of drugs can be studied by the topological index calculation. In this paper, we compute some reverse topological indices namely, the reverse general Randic index, the reverse atom bond connectivity index, the reverse geometric arithmetic index, the reverse forgotten index, the reverse Balaban index and the reverse Zagreb type indices. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the degree based topological properties of the novel planar metal-organic networks TM – TCNB. Interestingly, the TM – TCNB systems are metallic in any event in one turn heading and show long-run ferromagnetic coupling on the off chance that for attractive structures, which speak to perfect applicants and a fascinating possibility of uncommon applications in spintronics. Chemical graph theory plays an important role in modeling and designing any chemical structure. The topological indices are the numerical invariants of a molecular graph and are very useful for predicting their physical properties. We have computed the degree based topological indices for this metal-organic networks TM – TCNB. [ABSTRACT FROM AUTHOR]

In this article we discuss the reverse degree based topological indices for planar metal-organic networks like transition metal (TM) of the three-dimensional series such as: Ti, V, Cr, ... , or Zn, phthalocyanine, and tetracyanobenzene (TCNB) as free-standing sheets. In distinction, the TM-TCNB networks are metallic at least in one revolutionary orientation and demonstrate long-range ferromagnetic connect in case for magnetic erection, which illustrate ideal entrant and a stimulating prospect of unequaled applications in spintronics. Topological indices are numerical variables of a graph which describe its topology and are usually graph invariant. We have computed the reverse degree based topological indices like the reverse general Randic index, the reverse Balaban index, the reverse atom bond connectivity index, the reverse geometric index, the reverse Zagreb type indices, and the reverse augmented Zagreb index for this metal-organic networks TM-TCNB. [ABSTRACT FROM AUTHOR]

Topological indices are numerical parameters used to study the physical and chemical residences of compounds. Degree-based topological indices have been studied extensively and can be correlated with many properties of the understudy compounds. In the factors of degree-based topological indices, M-polynomial played an important role. In this paper, we derived closed formulas for some well-known degree-based topological indices like first and second Zagreb indices, the modified Zagreb index, the symmetric division index, the harmonic index, the Randić index and inverse Randić index, and the augmented Zagreb index using calculus. [ABSTRACT FROM AUTHOR]

An mk-graph of a graph G is defined by taking m ≥ 2 copies G1, ... , Gm of a graph G in which every vertex uh of copy Gh is adjacent to a corresponding vertex vm of copy Gm. An mk-graph is represented by mk(G). In this paper we work on some degree based connectivity indices of subdivided mk-graph generated by ladder and triangular ladder graph. Also closed formulas for computing various degree based topological indices of said families of graphs have been presented. [ABSTRACT FROM AUTHOR]

Network theory as an important role in the field of electronic and electrical engineering, for example, in signal processing, networking, communication theory, etc. The branch of mathematics known as Graph theory found remarkable applications in this area of study. A topological index (TI) is a real number attached with graph networks and correlates the chemical networks with many physical and chemical properties and chemical reactivity. The Optical Transpose Interconnection System (OTIS) network has received considerable attention in recent years and has a special place among real world architectures for parallel and distributed systems. In this report, we compute redefined first, second and third Zagreb indices of OTIS swapped and OTIS biswapped networks. We also compute some Zagreb polynomials of understudy Networks. [ABSTRACT FROM AUTHOR]

The nanostar dendrimers are a piece of another gathering of macromolecules that seem, by all accounts, to be photon pipes simply like counterfeit reception apparatuses. In addition, nanostar dendrimers are one of the fundamental stuffs of nanobiotechnology. The smart polymers are large-scale particles that show an emotional physioconcoction change because of little changes in their condition, for example, temperature, pH, light, attractive field, and ionic variables. A topological record of a graph G is a numeric quantity notorious with G which portrays subatomic diagram G. In this paper, we decide first and second Zagreb indices, hyper-Zagreb index, first multiple Zagreb index, second numerous Zagreb index, and Zagreb polynomials for nanostar dendrimer and smart polymer. [ABSTRACT FROM AUTHOR]

• Graph invariants are employed within the sciences of statistics, pattern recognition, computational geometry, biochemistry, and specifically chemicals to evaluate and construct data warehouses as well as chemical structures. • It is fascinating to see how numerous global features that have been established and developed within the paradigm of computational geometry present themselves in sophisticated connections. We examine the chemical graph of the crystal lattice of beryllium oxide (BeO) in this article. • Topological co-indices are crucial tools for investigations since they serve as molecular descriptors. Moreover, by connecting degree-based topological co-indices like, the first and second Zagreb co-indices, the atom bond connectivity co-index, the geometric arithmetic co-index, the forgotten co-index, the Balaban co-index, the augmented co-index, etc. • We can determine how much heat of formation was required to build these structures (BeO) by analysing the curve fitting methods for heat of formation. Graph invariants are employed within the sciences of statistics, pattern recognition, computational geometry, biochemistry, and specifically chemicals to evaluate and construct data warehouses as well as chemical structures. It is fascinating to see how numerous global features that have been established and developed within the paradigm of computational geometry present themselves in sophisticated connections. We examine the chemical graph of the crystal lattice of beryllium oxide (BeO) in this article. Topological co-indices are crucial tools for investigations since they serve as molecular descriptors. Moreover, by connecting degree-based topological co-indices like, the first and second Zagreb co-indices, the atom bond connectivity co-index, the geometric arithmetic co-index, the forgotten co-index, the Balaban co-index, the augmented co-index, etc. We can determine how much heat of formation was required to build these structures BeO by analysing the curve fitting methods for heat of formation. [ABSTRACT FROM AUTHOR]