scholarly journals Computation of Topological Indices of NEPS of Graphs

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Muhammad Imran ◽  
Shehnaz Akhter ◽  
Muhammad Kamran Jamil
Keyword(s):  
Structural Properties ◽  
Topological Indices ◽  
Research Topic ◽  
Theoretical Chemistry ◽  
Networks And Graphs ◽  
Graph Product ◽  
Zeroth Order ◽  
General Graph ◽  
Zagreb Indices ◽  
Numerical Invariants

The inspection of the networks and graphs through structural properties is a broad research topic with developing significance. One of the methods in analyzing structural properties is obtaining quantitative measures that encode data of the whole network by a real quantity. A large quantity of graph-associated numerical invariants has been used to examine the whole structure of networks. In this analysis, degree-related topological indices have a significant place in nanotechnology and theoretical chemistry. Thereby, the computation of indices is one of the successful branches of research. The noncomplete extended p -sum NEPS of graphs is a famous general graph product. In this paper, we investigated the exact formulas of general zeroth-order Randić, Randić, and the first multiplicative Zagreb indices for NEPS of graphs.

scholarly journals On Degree-Based Topological Indices for Strong Double Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Muhammad Rafiullah ◽  
Hafiz Muhammad Afzal Siddiqui ◽  
Muhammad Kamran Siddiqui ◽  
Mlamuli Dhlamini
Keyword(s):  
Structural Properties ◽  
Topological Index ◽  
Graphical Representation ◽  
Topological Indices ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Characteristic Value ◽  
3D Graphical Representation

A topological index is a characteristic value which represents some structural properties of a chemical graph. We study strong double graphs and their generalization to compute Zagreb indices and Zagreb coindices. We provide their explicit computing formulas along with an algorithm to generate and verify the results. We also find the relation between these indices. A 3D graphical representation and graphs are also presented to understand the dynamics of the aforementioned topological indices.

scholarly journals Predicting Some Physicochemical Properties of Octane Isomers: A Topological Approach Using ev-Degree and ve-Degree Zagreb Indices

2017 ◽  
Author(s):  
Süleyman Ediz
Keyword(s):  
Physicochemical Properties ◽  
Topological Indices ◽  
Theoretical Chemistry ◽  
Graph Invariants ◽  
Zagreb Index ◽  
Topological Approach ◽  
Zagreb Indices ◽  
Mathematical Properties ◽  
Octane Isomers ◽  
Mathematical Literature

Topological indices have important role in theoretical chemistry for QSPR researches. Among the all topological indices the Randić and the Zagreb indices have been used more considerably than any other topological indices in chemical and mathematical literature. Most of the topological indices as in the Randić and the Zagreb indices are based on the degrees of the vertices of a connected graph. Recently novel two degree concepts have been defined in graph theory; ev-degrees and ve-degrees. In this study we define ev-degree Zagreb index, ve-degree Zagreb indices and ve-degree Randić index by using these new graph invariants as parallel to their corresponding classical degree versions. We compare these new group ev-degree and ve-degree indices with the other well-known and most used topological indices in literature such as; Wiener, Zagreb and Randić indices by modelling some physicochemical properties of octane isomers. We show that the ev-degree Zagreb index, the ve-degree Zagreb and the ve-degree Randić indices give better correlation than Wiener, Zagreb and Randić indices to predict the some specific physicochemical properties of octanes. We investigate the relations between the second Zagreb index and ev-degree and ve-degree Zagreb indices and some mathematical properties of ev-degree and ve-degree Zagreb indices.

scholarly journals Forgotten Index of Generalized Operations on Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Muhammad Javaid ◽  
Saira Javed ◽  
Saima Q. Memon ◽  
Abdulaziz Mohammed Alanazi
Keyword(s):  
Structural Properties ◽  
Topological Indices ◽  
Theoretical Chemistry ◽  
Factor Graphs ◽  
Molecular Graphs ◽  
Strong Product ◽  
Forgotten Index ◽  
Counting Polynomial ◽  
Product Of Graphs

In theoretical chemistry, several distance-based, degree-based, and counting polynomial-related topological indices (TIs) are used to investigate the different chemical and structural properties of the molecular graphs. Furtula and Gutman redefined the F -index as the sum of cubes of degrees of the vertices of the molecular graphs to study the different properties of their structure-dependency. In this paper, we compute F -index of generalized sum graphs in terms of various TIs of their factor graphs, where generalized sum graphs are obtained by using four generalized subdivision-related operations and the strong product of graphs. We have analyzed our results through the numerical tables and the graphical presentations for the particular generalized sum graphs constructed with the help of path (alkane) graphs.

scholarly journals Mathematical Properties of Variable Topological Indices

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 43
Author(s):  
José M. Sigarreta
Keyword(s):  
Real Number ◽  
Large Class ◽  
Symmetric Functions ◽  
Topological Indices ◽  
Current Interest ◽  
Zagreb Indices ◽  
Mathematical Properties ◽  
Connectivity Indices ◽  
Optimal Bounds ◽  
New Framework

A topic of current interest in the study of topological indices is to find relations between some index and one or several relevant parameters and/or other indices. In this paper we study two general topological indices Aα and Bα, defined for each graph H=(V(H),E(H)) by Aα(H)=∑ij∈E(H)f(di,dj)α and Bα(H)=∑i∈V(H)h(di)α, where di denotes the degree of the vertex i and α is any real number. Many important topological indices can be obtained from Aα and Bα by choosing appropriate symmetric functions and values of α. This new framework provides new tools that allow to obtain in a unified way inequalities involving many different topological indices. In particular, we obtain new optimal bounds on the variable Zagreb indices, the variable sum-connectivity index, the variable geometric-arithmetic index and the variable inverse sum indeg index. Thus, our approach provides both new tools for the study of topological indices and new bounds for a large class of topological indices. We obtain several optimal bounds of Aα (respectively, Bα) involving Aβ (respectively, Bβ). Moreover, we provide several bounds of the variable geometric-arithmetic index in terms of the variable inverse sum indeg index, and two bounds of the variable inverse sum indeg index in terms of the variable second Zagreb and the variable sum-connectivity indices.

scholarly journals On the Multiplicative Degree-Based Topological Indices of Silicon-Carbon Si2C3-I[p,q] and Si2C3-II[p,q]

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 320 ◽  
Author(s):  
Young Kwun ◽  
Abaid Virk ◽  
Waqas Nazeer ◽  
M. Rehman ◽  
Shin Kang
Keyword(s):  
Molecular Structure ◽  
Graph Theory ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Topological Indices ◽  
Molecular Compound ◽  
Zagreb Indices ◽  
Silicon Carbon ◽  
Physico Chemical ◽  
Structure Research

The application of graph theory in chemical and molecular structure research has far exceeded people’s expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonds by edges. Topological indices help us to predict many physico-chemical properties of the concerned molecular compound. In this article, we compute Generalized first and multiplicative Zagreb indices, the multiplicative version of the atomic bond connectivity index, and the Generalized multiplicative Geometric Arithmetic index for silicon-carbon Si2C3−I[p,q] and Si2C3−II[p,q] second.

scholarly journals Computation of Zagreb and atom-bond connectivity indices of certain families of dendrimers by using automorphism group action

2017 ◽  
Vol 82 (2) ◽  
pp. 151-162
Author(s):  
Uzma Ahmad ◽  
Sarfraz Ahmad ◽  
Rabia Yousaf
Keyword(s):  
Automorphism Group ◽  
Carbon Atom ◽  
Physicochemical Properties ◽  
Group Action ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Zagreb Indices ◽  
Connectivity Indices ◽  
Atom Bond

In QSAR/QSPR studies, topological indices are utilized to predict the bioactivity of chemical compounds. In this paper, the closed forms of different Zagreb indices and atom?bond connectivity indices of regular dendrimers G[n] and H[n] in terms of a given parameter n are determined by using the automorphism group action. It was reported that these connectivity indices are correlated with some physicochemical properties and are used to measure the level of branching of the molecular carbon-atom skeleton.

scholarly journals Zagreb Polynomials and redefined Zagreb indices of nanostar dendrimers

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 31-40 ◽  
Author(s):  
Shin Min Kang ◽  
Muhammad Yousaf ◽  
Manzoor Ahmad Zahid ◽  
Muhammad Younas ◽  
Waqas Nazeer
Keyword(s):  
Boiling Point ◽  
Strain Energy ◽  
Chemical Properties ◽  
Topological Indices ◽  
Central Core ◽  
Zagreb Indices ◽  
Physico Chemical

Abstract Dendrimers are profoundly extended natural macromolecules with successive layers of branch units encompassing a central core. Topological indicess are numbers related with graph of a compound to allow quantitative structureactivity/property/lethality connections. These topological indices relate certain physico-chemical properties like stability, boiling point, strain energy and so forth of a compound. In this report, there have been computed redefined first, second and third Zagreb indices of Nanostar dendrimers. The authors also analyzed some Zagreb polynomials of understudy dendrimers.

scholarly journals Some Eccentricity-Based Topological Indices and Polynomials of Poly(EThyleneAmidoAmine) (PETAA) Dendrimers

Processes ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 433 ◽  
Author(s):  
Jialin Zheng ◽  
Zahid Iqbal ◽  
Asfand Fahad ◽  
Asim Zafar ◽  
Adnan Aslam ◽  
...  
Keyword(s):  
Molecular Descriptors ◽  
Molecular Graph ◽  
Topological Indices ◽  
Molecular Structures ◽  
Connectivity Index ◽  
Connectivity Indices ◽  
Numerical Invariants ◽  
Explicit Representations ◽  
Pharmaceutical Properties

Topological indices have been computed for various molecular structures over many years. These are numerical invariants associated with molecular structures and are helpful in featuring many properties. Among these molecular descriptors, the eccentricity connectivity index has a dynamic role due to its ability of estimating pharmaceutical properties. In this article, eccentric connectivity, total eccentricity connectivity, augmented eccentric connectivity, first Zagreb eccentricity, modified eccentric connectivity, second Zagreb eccentricity, and the edge version of eccentric connectivity indices, are computed for the molecular graph of a PolyEThyleneAmidoAmine (PETAA) dendrimer. Moreover, the explicit representations of the polynomials associated with some of these indices are also computed.

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 $BN_{m}^{n}$.

On Topological Properties of 2-Dimensional Lattices of Carbon Nanotubes

2016 ◽  
Vol 13 (10) ◽  
pp. 6606-6615
Author(s):  
Sakander Hayat ◽  
Muhammad Kashif Shafiq ◽  
Asad Khan ◽  
Hassan Raza ◽  
Hafiz Muhmmad Afzal Siddiqui ◽  
...  
Keyword(s):  
Carbon Nanotubes ◽  
Quaternary Structure ◽  
Topological Indices ◽  
Topological Descriptors ◽  
Structure Property ◽  
Specific Chemical ◽  
Carbon Nanosheets ◽  
Chemical Significance ◽  
Numerical Invariants ◽  
Intermediate Size

Topological descriptors are the most important numerical quantities in the fields of mathematical chemistry and nanotechnology. These numerical descriptors are based on the topology of the atoms and their bonds (chemical conformation, quaternary structure). Local-valency/degree based topological descriptors/indices are of vital importance due to their specific chemical significance. These numerical invariants are the most successful molecular descriptors in structure-property and structure-activity relationships studies. A nanostructure is an object of intermediate size between molecular and microscopic structures. It is a product derived through engineering at the molecular scale. The most important of these new materials are carbon nanotubes. They have remarkable electronic properties and many other unique characteristics. Carbon nanosheets are 2-dimensional lattices of carbon nanotubes. To compute and study topological indices of nanostructures is a respected problem in nanotechnology. In this paper, degree based topological indices of certain carbon nanosheets are strong-minded. We formulate an important conjecture at the end of this article.

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