On the Certain Topological Indices of Titania Nanotube TiO2[m, n]

2017 ◽  
Vol 72 (7) ◽  
pp. 647-654 ◽  
Author(s):  
M. Javaid ◽  
Jia-Bao Liu ◽  
M. A. Rehman ◽  
Shaohui Wang
Keyword(s):  
Chemical Compound ◽  
Topological Index ◽  
Molecular Graph ◽  
Topological Indices ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Mathematical Expressions ◽  
Titania Nanotube ◽  
Physical Features ◽  
Atom Bond

AbstractA numeric quantity that characterises the whole structure of a molecular graph is called the topological index that predicts the physical features, chemical reactivities, and boiling activities of the involved chemical compound in the molecular graph. In this article, we give new mathematical expressions for the multiple Zagreb indices, the generalised Zagreb index, the fourth version of atom-bond connectivity (ABC4) index, and the fifth version of geometric-arithmetic (GA5) index of TiO2[m, n]. In addition, we compute the latest developed topological index called by Sanskruti index. At the end, a comparison is also included to estimate the efficiency of the computed indices. Our results extended some known conclusions.

scholarly journals General Fifth M- Zagreb Polynomials of the TUC4C8(R)[p, q] 2D-Lattice and its Derived Graphs

2020 ◽  
Vol 10 (1) ◽  
pp. 1738-1747
Keyword(s):  
Chemical Compound ◽  
Molecular Graph ◽  
Vital Role ◽  
Topological Indices ◽  
Line Graphs ◽  
Topological Properties ◽  
Zagreb Index ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Physical Chemical

A molecular graph or a chemical graph is a graph related to the structure of a chemical compound. The topological indices play a vital role in understanding the physical, chemical, and topological properties of the respective compound. ln this article, we discuss the computation of the degree-based topological indices, namely - the fifth M-Zagreb indices and their polynomials, fifth hyper M-Zagreb indices and their polynomials, general fifth M-Zagreb indices and their polynomials, third Zagreb index and it is polynomial for the TUC_4 C_8 (R)[p,q] lattice, its subdivision, and para-line graphs.

scholarly journals Valency-based molecular descriptors of Bakelite network BNmn$B\text N_{m}^{n}$

2019 ◽  
Vol 17 (1) ◽  
pp. 663-670 ◽  
Author(s):  
Maqsood Ahmad ◽  
Muhammad Javaid ◽  
Muhammad Saeed ◽  
Chahn Yong Jung
Keyword(s):  
Physical Properties ◽  
Molecular Descriptors ◽  
Molecular Graph ◽  
Synthetic Polymer ◽  
Topological Indices ◽  
Qsar Studies ◽  
Zagreb Indices ◽  
Symmetric Division ◽  
Atom Bond

AbstractBakelite network $BN_{m}^{n}$is a molecular graph of bakelite, a pioneering and revolutionary synthetic polymer (Thermosetting Plastic) and regarded as the material of a thousand uses. In this paper, we aim to compute various degree-based topological indices of a molecular graph of bakelite network $BN_{m}^{n}$. These molecular descriptors play a fundamental role in QSPR/QSAR studies in describing the chemical and physical properties of Bakelite network $BN_{m}^{n}$. We computed atom-bond connectivity ABC its fourth version ABC4 geometric arithmetic GA its fifth version GA5 Narumi-Katayama, sum-connectivity and Sanskruti indices, first, second, modified and augmented Zagreb indices, inverse and general Randic’ indices, symmetric division, harmonic and inverse sum indices of $BN_{m}^{n}$.

scholarly journals On Computation Degree-Based Topological Descriptors for Planar Octahedron Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Wang Zhen ◽  
Parvez Ali ◽  
Haidar Ali ◽  
Ghulam Dustigeer ◽  
Jia-Bao Liu
Keyword(s):  
Graph Theory ◽  
Chemical Compound ◽  
Topological Index ◽  
Molecular Graph ◽  
Topological Descriptors ◽  
Zagreb Index ◽  
Chemical Graph ◽  
Symmetric Division ◽  
Chemical Graph Theory ◽  
Augmented Zagreb Index

A molecular graph is used to represent a chemical molecule in chemical graph theory, which is a branch of graph theory. A graph is considered to be linked if there is at least one link between its vertices. A topological index is a number that describes a graph’s topology. Cheminformatics is a relatively young discipline that brings together the field of sciences. Cheminformatics helps in establishing QSAR and QSPR models to find the characteristics of the chemical compound. We compute the first and second modified K-Banhatti indices, harmonic K-Banhatti index, symmetric division index, augmented Zagreb index, and inverse sum index and also provide the numerical results.

On the First and Second Zagreb and First and Second Hyper-Zagreb Indices of Carbon Nanocones CNCk[n]

2016 ◽  
Vol 13 (10) ◽  
pp. 7475-7482 ◽  
Author(s):  
Wei Gao ◽  
Mohammad Reza Farahani ◽  
Muhammad Kamran Siddiqui ◽  
Muhammad Kamran Jamil
Keyword(s):  
Molecular Graph ◽  
Topological Indices ◽  
Zagreb Index ◽  
Carbon Nanocones ◽  
Zagreb Indices ◽  
Minimum Path ◽  
Multiple Edges

Let G be a simple molecular graph without directed and multiple edges and without loops, the vertex and edge-sets of which are represented by V(G) and E(G), respectively. Suppose G is a connected molecular graph and vertices u, v ∈ V(>G). The distance dG(u,v) (or d(u,v) for short) between vertices u and V of G is defined as the length of a minimum path between u and V. The first and second Zagreb indices of a graph G are defined as M1(G) = ΣE=uv∈E(G)(dV+dV) and M2(G) = ΣE=uv∈E(G)(dV×dv) where du and dv are the degree of the vertices u and V of G. Recently the Hyper-Zagreb index of a graph G is defined as HM(G) = ΣE=uv∈E(G)(dV+dV)2, by Shirdel et al. In this paper, we define a new version of Zagreb topological indices, on based the Hyper-Zagreb index that defined as the sum of the weights (dudV)2 and the Second Hyper-Zagreb index of G is equal to HM2(G) = ΣE=uv∈E(G)(dVdV)22. In continue, exact formulas for the first and second Zagreb and Hyper-Zagreb indices of Carbon Nanocones CNCk[n] are computed.

scholarly journals Edge Version Molecular Descriptors of Tetrameric 1, 3 Adamantane

2018 ◽  
Vol 7 (4.10) ◽  
pp. 403
Author(s):  
G. Mohanappriya ◽  
D. Vijiyalakshmi
Keyword(s):  
Molecular Descriptors ◽  
Molecular Graph ◽  
Topological Indices ◽  
Connectivity Index ◽  
Zagreb Index ◽  
Numerical Invariants ◽  
Atom Bond

Molecular descriptors (Topological indices) are the numerical invariants of a molecular graph which distinguish its topology. In this article, we compute edge version of topological indices such as Zagreb index, Atom bond connectivity index, Fourth atom bond connectivity index, Geometric Arithmetic index and Fifth Geometric Arithmetic index of tetrameric 1,3 adamantane. 

scholarly journals On Topological Indices of Dual Graph of Benzene Ring Embedded in P-Type Surface in 2D Network

2021 ◽  
Vol 10 (3) ◽  
pp. 1936-1941
Keyword(s):  
Benzene Ring ◽  
Molecular Graph ◽  
Dual Graph ◽  
Topological Indices ◽  
Zagreb Indices ◽  
Abc Index ◽  
P Type ◽  
2D Network ◽  
Ga Index ◽  
Atom Bond

The structure of any finite molecular graph which represent numerical quantities are known as topological indices. The importance of topological indices is generally linked with QSAR/QSPR. In this paper, we compute general Zagreb (M஑_) index, general Randic connectivity (R஑_) index, general sum-connectivity (χ஑) index, atom-bond connectivity (ABC) index, and geometric-arithmetic (GA) index,ABCସ, GAହ, multiple Zagreb indices and Zagreb polynomial indices of the of dual graph of benzene ring embedded in P-type-surface in 2D network.

scholarly journals The Topological Indices of the Non-commuting Graph for Symmetric Groups

2020 ◽  
pp. 1-5
Author(s):  
Nur Idayu Alimon ◽  
Nor Haniza Sarmin ◽  
Ahmad Erfanian
Keyword(s):  
Symmetric Group ◽  
Chemical Compound ◽  
Molecular Graph ◽  
Symmetric Groups ◽  
Wiener Index ◽  
Topological Indices ◽  
Zagreb Index ◽  
Commuting Graph ◽  
Central Elements ◽  
Vertex Set

Topological indices are the numerical values that can be calculated from a graph and it is calculated based on the molecular graph of a chemical compound. It is often used in chemistry to analyse the physical properties of the molecule which can be represented as a graph with a set of vertices and edges. Meanwhile, the non-commuting graph is the graph of vertex set whose vertices are non-central elements and two distinct vertices are joined by an edge if they do not commute. The symmetric group, denoted as S_n, is a set of all permutation under composition. In this paper, two of the topological indices, namely the Wiener index and the Zagreb index of the non-commuting graph for symmetric groups of order 6 and 24 are determined. Keywords: Wiener index; Zagreb index; non-commuting graph; symmetric groups

scholarly journals Molecular Properties of Symmetrical Networks Using Topological Polynomials

2019 ◽  
Vol 17 (1) ◽  
pp. 849-864 ◽  
Author(s):  
Xing-Long Wang ◽  
Jia-Bao Liu ◽  
Maqsood Ahmad ◽  
Muhammad Kamran Siddiqui ◽  
Muhammad Hussain ◽  
...  
Keyword(s):  
Topological Index ◽  
Molecular Graph ◽  
Chemical Species ◽  
Chemical Properties ◽  
Biological Properties ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Physico Chemical ◽  
Symmetry Properties ◽  
Physical Features

AbstractA numeric quantity that comprehend characteristics of molecular graph Γ of chemical compound is known as topological index. This number is, in fact, invariant with respect to symmetry properties of molecular graph Γ. Many researchers have established, after diverse studies, a parallel between the physico chemical properties like boiling point, stability, similarity, chirality and melting point of chemical species and corresponding chemical graph. These descriptors defined on chemical graphs are extremely helpful for researchers to conduct regression model like QSAR/QSPR and better understand the physical features, complexity of molecules, chemical and biological properties of underlying compound.In this paper, several structure descriptors of vital importance, namely, first, second, modified and augmented Zagreb indices, inverse and general Randic indices, symmetric division, harmonic, inverse sum and forgotten indices of Hex-derived Meshes (networks) of two kinds, namely, HDN1(n) and HDN2(n) are computed and recovered using general approach of topological polynomials.

scholarly journals Computing Topological Indices and Polynomials for Line Graphs

Mathematics ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 137 ◽  
Author(s):  
Shahid Imran ◽  
Muhammad Siddiqui ◽  
Muhammad Imran ◽  
Muhammad Nadeem
Keyword(s):  
Topological Index ◽  
Line Graph ◽  
Topological Indices ◽  
Line Graphs ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Second Zagreb Index ◽  
Vertex Degrees ◽  
Set Up ◽  
Ladder Graphs

A topological index is a number related to the atomic index that allows quantitative structure–action/property/toxicity connections. All the more vital topological indices correspond to certain physico-concoction properties like breaking point, solidness, strain vitality, and so forth, of synthetic mixes. The idea of the hyper Zagreb index, multiple Zagreb indices and Zagreb polynomials was set up in the substance diagram hypothesis in light of vertex degrees. These indices are valuable in the investigation of calming exercises of certain compound systems. In this paper, we computed the first and second Zagreb index, the hyper Zagreb index, multiple Zagreb indices and Zagreb polynomials of the line graph of wheel and ladder graphs by utilizing the idea of subdivision.

scholarly journals Connection-Based Multiplicative Zagreb Indices of Dendrimer Nanostars

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Aqsa Sattar ◽  
Muhammad Javaid ◽  
Ebenezer Bonyah
Keyword(s):  
Graph Theory ◽  
Physicochemical Properties ◽  
Topological Index ◽  
Molecular Graph ◽  
Topological Indices ◽  
Zagreb Indices ◽  
Mathematical Chemistry ◽  
Chemical Structures ◽  
And Mathematics

The field of graph theory is broadly growing and playing a remarkable role in cheminformatics, mainly in chemistry and mathematics in developing different chemical structures and their physicochemical properties. Mathematical chemistry provides a platform to study these physicochemical properties with the help of topological indices (TIs). A topological index (TI) is a function that connects a numeric number to each molecular graph. Zagreb indices (ZIs) are the most studied TIs. In this paper, we establish general expressions to calculate the connection-based multiplicative ZIs, namely, first multiplicative ZIs, second multiplicative ZIs, third multiplicative ZIs, and fourth multiplicative ZIs, of two renowned dendrimer nanostars. The defined expressions just depend on the step of growth of these dendrimers. Moreover, we have compared our calculated for both type of dendrimers with each other.

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