On Topological Indices of Dual Graph of Benzene Ring Embedded in P-Type Surface in 2D Network (original) (raw)
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Topological Indices of Derived Networks of Benzene Ring Embedded in P -Type Surface on 2 D
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Topological index (TI) is a numerical number assigned to the molecular structure that is used for correlation analysis in pharmacology, toxicology, and theoretical and environmental chemistry. Benzene ring embedded in the P -type surface on 2 D network has stability similar to C 60 and can be defined as 3 D linkage of C 8 rings. This structure is the simplest possible tilling of the periodic minimal surface P which contains one type of carbon atom. In this paper, we compute general Randić, general Zagreb, general sum-connectivity, first Zagreb, second Zagreb, and A B C and G A indices of two operations (simple medial and stellation) of 2 D network of benzene ring. Also, the exact expressions of A B C 4 and G A 5 indices of these structures are computed.
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Algebraic polynomials play an important role in theoretical chemistry because these can reflect the properties of the chemical compound. M-polynomial is also an algebraic polynomial that is used to find the expressions of several degree dependent topological indices. These topological indices have the ability to explore the information store in the chemical molecule. In this work, we computed the M-polynomial and then obtained the degree-based topological indices for the benzene ring embedded in P-type-surface in 2D network. We also explored the results graphically.
General Fifth M-Zagreb Polynomials of Benzene Ring Implanted in the P-Type-Surface in 2D Network
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Constitutional formulae of molecules are molecular graphs consisting of atoms as vertices and bonds between them represented as edges. The various physical, chemical, and biological properties of molecules are dependent on their molecular structures. The molecular structure is most important, not only to chemists but also to all scientists. The molecular structure descriptors or topological indices of molecules are a mathematical number or a set of selected invariants of matrices that are used to Quantitative Structure-Activity (-Property) Relationships (QSAR/QSPR) studies. In this paper, we computed some new degree-based topological indices of benzene ring implanted in the P-type-surface in the 2D network and its line subdivision of graph.
Topological properties of Graphene using some novel neighborhood degree-based topological indices
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Topological indices are numeric quantities that transform chemical structure to real number. Topological indices are used in QSAR/QSPR studies to correlate the bioactivity and physiochemical properties of molecule. In this paper, some newly designed neighborhood degree-based topological indices named as neighborhood Zagreb index ([Formula: see text]), neighborhood version of Forgotten topological index ([Formula: see text]), modified neighborhood version of Forgotten topological index ([Formula: see text]), neighborhood version of second Zagreb index ([Formula: see text]) and neighborhood version of hyper Zagreb index ([Formula: see text]) are obtained for Graphene and line graph of Graphene using subdivision idea. In addition, these indices are compared graphically with respect to their response for Graphene and line graph of subdivision of Graphene.
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Graphene is one of the most promising nanomaterial because of its unique combination of superb properties, which opens a way for its exploitation in a wide spectrum of applications ranging from electronics to optics, sensors, and bio devices. Inspired by recent work on Graphene of computing topological indices, here we compute new topological indices viz. Arithmetic-Geometric index (AG2 index), SK3 index and Sanskruti index of a molecular graph G and obtain the explicit formulae of these indices for Graphene.
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A Topological index also known as connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as Randi c ´ , atom-bond connectivity (ABC) and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study HDCN1(m,n) and HDCN2(m,n) of dimension m , n and derive analytical closed results of general Randi c ´ index R α ( G ) for different values of α . We also compute the general first Zagreb, ABC, GA, A B C 4 and G A 5 indices for these Hex derived cage networks for the first time and give closed formulas of these degree-based indices.
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Topological indices are very useful to assume certain physiochemical properties of the chemical compound. A molecular descriptor which changes the molecular structures into certain real numbers is said to be a topological index. In chemical graph theory, to create quantitative structure activity relationships in which properties of molecule may be linked with their chemical structures relies greatly on topological indices. The benzene molecule is a common chemical shape in chemistry, physics, and nanoscience. This molecule could be very beneficial to synthesize fragrant compounds. The circumcoronene collection of benzenoid H m is one family that generates from benzene molecules. The purpose of this study is to calculate the topological indices of the double and strong double graphs of the circumcoronene series of benzenoids H m . In addition, we also present a numerical and graphical comparison of topological indices of the double and strong double graphs of the circumcoronene serie...
Topological Indices of Certain Transformed Chemical Structures
Journal of Chemistry, 2020
Topological indices like generalized Randić index, augmented Zagreb index, geometric arithmetic index, harmonic index, product connectivity index, general sum-connectivity index, and atom-bond connectivity index are employed to calculate the bioactivity of chemicals. In this paper, we define these indices for the line graph of k-subdivided linear [n] Tetracene, fullerene networks, tetracenic nanotori, and carbon nanotube networks.
Neighbourhood Degree – Based Topological Indices of Graphene Structure
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The theory of chemical reaction networks is a branch of mathematics that aims to mimic real-world behavior. This research area has drawn many researchers' attention, primarily due to its biological and empirical chemistry applications. The fascinating problems that emerge from the mathematical structures involved have kindled the interest of pure mathematicians. In this paper, we estimate a few topological indices such as SK index, SK1 index, SK2 index, Modified Randić index, and Inverse Sum Index for the Graphene structure based on the neighborhood degree and obtain results based on both sum and products of the cardinality of edge partitions corresponding to 4 different Graphene structures. We also present the 3D representations of the indices using MATLAB.
Some new degree based topological indices via M-polynomial
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Algebraic polynomials play an important role in theoretical chemistry because these can reflect the properties of the chemical compound. M-polynomial is also an algebraic polynomial that is used to find the expressions of several degree dependent topological indices. These topological indices have the ability to explore the information store in the chemical molecule. In this work, we computed the M-polynomial and then obtained the degree-based topological indices for the benzene ring embedded in P-type-surface in 2D network. We also explored the results graphically. KEYWORDS Benzene ring embedded in P-type surface in 2D network; graph polynomial; M-polynomial; chemical molecule; degree dependent topological indices.