scholarly journals On Certain Aspects of Topological Indices

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Tanweer Ul Islam ◽  
Zeeshan Saleem Mufti ◽  
Aqsa Ameen ◽  
Muhammad Nauman Aslam ◽  
Ali Tabraiz
Keyword(s):  
Topological Index ◽  
Molecular Graph ◽  
Topological Indices ◽  
Connectivity Index ◽  
General Version ◽  
Zagreb Index ◽  
Harmonic Index ◽  
Degree Distance ◽  
Apex Graph ◽  
Structure Descriptor

A topological index, also known as connectivity index, is a molecular structure descriptor calculated from a molecular graph of a chemical compound which characterizes its topology. Various topological indices are categorized based on their degree, distance, and spectrum. In this study, we calculated and analyzed the degree-based topological indices such as first general Zagreb index M r G , geometric arithmetic index GA G , harmonic index H G , general version of harmonic index H r G , sum connectivity index λ G , general sum connectivity index λ r G , forgotten topological index F G , and many more for the Robertson apex graph. Additionally, we calculated the newly developed topological indices such as the AG 2 G and Sanskruti index for the Robertson apex graph G.

scholarly journals Relating the ABC and harmonic indices

2014 ◽  
Vol 79 (5) ◽  
pp. 557-563 ◽  
Author(s):  
Ivan Gutman ◽  
Lingping Zhong ◽  
Kexiang Xu
Keyword(s):  
Molecular Structure ◽  
Topological Index ◽  
Molecular Graph ◽  
Vertex Degree ◽  
Harmonic Index ◽  
Abc Index ◽  
Atom Bond ◽  
Structure Descriptor

The atom-bond connectivity (ABC) index is a much-studied molecular structure descriptor, based on the degrees of the vertices of the molecular graph. Recently, another vertex-degree-based topological index - the harmonic index (H) - attracted attention and gained popularity. We show how ABC and H are related.

scholarly journals Topological Indices of Certain Transformed Chemical Structures

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Xuewu Zuo ◽  
Jia-Bao Liu ◽  
Hifza Iqbal ◽  
Kashif Ali ◽  
Syed Tahir Raza Rizvi
Keyword(s):  
Carbon Nanotube ◽  
Line Graph ◽  
Topological Indices ◽  
Connectivity Index ◽  
Zagreb Index ◽  
Harmonic Index ◽  
Chemical Structures ◽  
Augmented Zagreb Index ◽  
Carbon Nanotube Networks ◽  
Atom Bond

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.

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 the Computation of Some Topological Descriptors to Find Closed Formulas for Certain Chemical Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Muhammad Haroon Aftab ◽  
Muhammad Rafaqat ◽  
M. Hussain ◽  
Tariq Zia
Keyword(s):  
Research Paper ◽  
Topological Indices ◽  
Connectivity Index ◽  
Topological Descriptors ◽  
General Version ◽  
Harmonic Index ◽  
Chemical Graphs ◽  
Abc Index ◽  
Atom Bond ◽  
Honeycomb Network

In this research paper, we will compute the topological indices (degree based) such as the ordinary generalized geometric-arithmetic (OGA) index, first and second Gourava indices, first and second hyper-Gourava indices, general Randic´ index R γ G , for  γ = ± 1 , ± 1 / 2 , harmonic index, general version of the harmonic index, atom-bond connectivity (ABC) index, SK, SK1, and SK2 indices, sum-connectivity index, general sum-connectivity index, and first general Zagreb and forgotten topological indices for various types of chemical networks such as the subdivided polythiophene network, subdivided hexagonal network, subdivided backbone DNA network, and subdivided honeycomb network. The discussion on the aforementioned networks will give us very remarkable results by using the aforementioned topological indices.

scholarly journals Topological Indices of Vitamin D3

2018 ◽  
Vol 7 (4) ◽  
pp. 6276
Author(s):  
Rajesh Kanna ◽  
Roopa S ◽  
PARASHIVAMURTHY H L
Keyword(s):  
Vitamin D3 ◽  
Topological Index ◽  
Topological Indices ◽  
Connectivity Index ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Second Zagreb Index ◽  
Augmented Zagreb Index ◽  
Abc Index ◽  
Ga Index

Graph theory has provided chemists with a variety of useful tools, such as topological indices. A topological index Top(G) of a graph G is a number with the property that for every graph H isomorphic to G, Top(H) = Top(G). In this paper, we compute ABC index, ABC4 index, Randi´c connectivity index, Sum connectivity index, GA index , GA5 index, First Zagreb index, Second Zagreb index, First Multiple Zagreb index, Second Multiple Zagreb index, Augmented Zagreb index, Harmonic index and Hyper Zagreb index, First Zagreb polynomial, Second Zagreb polynomial, Third Zagreb polynomial, Forgotten polynomials, Forgotten topological index and Symmetric division index of vitamin D3.

scholarly journals The Calculations of Topological Indices on Certain Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Jia-Bao Liu ◽  
Ting Zhang ◽  
Sakander Hayat
Keyword(s):  
Topological Index ◽  
Molecular Graph ◽  
Topological Indices ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Chemical Graph ◽  
The Core ◽  
Chemical Graph Theory ◽  
Definition Of ◽  
Internal Relationship

It is one of the core problems in the study of chemical graph theory to study the topological index of molecular graph and the internal relationship between its structural properties and some invariants. In recent years, topological index has been gradually applied to the models of QSAR and QSPR . In this work, using the definition of the ABC index, AZI index, GA index, the multiplicative version of ordinary first Zagreb index, the second multiplicative Zagreb index, and Zagreb index, we calculate the degree-based topological indices of some networks. Then, the above indices’ formulas are obtained.

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 Vertex-Based Topological Indices of Double and Strong Double Graph of Dutch Windmill Graph

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Muhammad Asad Ali ◽  
Muhammad Shoaib Sardar ◽  
Imran Siddique ◽  
Dalal Alrowaili
Keyword(s):  
Graph Theory ◽  
Chemical Properties ◽  
Topological Indices ◽  
Connectivity Index ◽  
Vaporization Enthalpy ◽  
Zagreb Index ◽  
Graph Operations ◽  
Big Graphs ◽  
Physical And Chemical ◽  
Atom Bond

A measurement of the molecular topology of graphs is known as a topological index, and several physical and chemical properties such as heat formation, boiling point, vaporization, enthalpy, and entropy are used to characterize them. Graph theory is useful in evaluating the relationship between various topological indices of some graphs derived by applying certain graph operations. Graph operations play an important role in many applications of graph theory because many big graphs can be obtained from small graphs. Here, we discuss two graph operations, i.e., double graph and strong double graph. In this article, we will compute the topological indices such as geometric arithmetic index GA , atom bond connectivity index ABC , forgotten index F , inverse sum indeg index ISI , general inverse sum indeg index ISI α , β , first multiplicative-Zagreb index PM 1   and second multiplicative-Zagreb index PM 2 , fifth geometric arithmetic index GA 5 , fourth atom bond connectivity index ABC 4 of double graph, and strong double graph of Dutch Windmill graph D 3 p .

scholarly journals Topological properties of Graphene using some novel neighborhood degree-based topological indices

2019 ◽  
Vol 11 (01) ◽  
pp. 1950006 ◽  
Author(s):  
Sourav Mondal ◽  
Nilanjan De ◽  
Anita Pal
Keyword(s):  
Real Number ◽  
Chemical Structure ◽  
Topological Index ◽  
Line Graph ◽  
Topological Indices ◽  
Index Formula ◽  
Topological Properties ◽  
Zagreb Index ◽  
Physiochemical Properties ◽  
Second Zagreb Index

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.

scholarly journals On Some New Neighborhood Degree-Based Indices for Some Oxide and Silicate Networks

J ◽  
2019 ◽  
Vol 2 (3) ◽  
pp. 384-409
Author(s):  
Sourav Mondal ◽  
Nilanjan De ◽  
Anita Pal
Keyword(s):  
Molecular Structure ◽  
Network Theory ◽  
Topological Index ◽  
Applied Mathematics ◽  
Reaction Network ◽  
Topological Indices ◽  
Zagreb Index ◽  
Second Zagreb Index ◽  
Real World Problems ◽  
Chemical Reaction Network Theory

Topological indices are numeric quantities that describes the topology of molecular structure in mathematical chemistry. An important area of applied mathematics is the chemical reaction network theory. Real-world problems can be modeled using this theory. Due to its worldwide applications, chemical networks have attracted researchers since their foundation. In this report, some silicate and oxide networks are studied, and exact expressions of some newly-developed neighborhood degree-based topological indices named as the neighborhood Zagreb index ( M N ), the neighborhood version of the forgotten topological index ( F N ), the modified neighborhood version of the forgotten topological index ( F N ∗ ), the neighborhood version of the second Zagreb index ( M 2 ∗ ), and neighborhood version of the hyper Zagreb index ( H M N ) are obtained for the aforementioned networks. In addition, a comparison among all the indices is shown graphically.

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