M-Polynomials and Degree-Based Topological Indices of the Molecule Copper(I) Oxide

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.

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Certain topological indices and polynomials for the semitotal-point graph and line graph of semitotal-point graph for Dutch windmill graph

Indonesian Journal of Combinatorics ◽

10.19184/ijc.2019.3.2.1 ◽

2020 ◽

Vol 3 (2) ◽

pp. 63

Author(s):

Salma Kanwal ◽

Mariam Imtiaz ◽

Ayesha Manzoor ◽

Nazeeran Idrees ◽

Ammara Afzal

Keyword(s):

Line Graph ◽

Topological Indices ◽

Point Graph ◽

Zagreb Index ◽

Harmonic Index ◽

Zagreb Indices ◽

Symmetric Division ◽

Augmented Zagreb Index ◽

Forgotten Index

Dutch windmill graph [1, 2] and denoted by Dnm. Order and size of Dutch windmill graph are (n−1)m+1 and mn respectively. In this paper, we computed certain topological indices and polynomials i.e. Zagreb polynomials, hyper Zagreb, Redefined Zagreb indices, modified first Zagreb, Reduced second Zagreb, Reduced Reciprocal Randi´c, 1st Gourava index, 2nd Gourava index, 1st hyper Gourava index, 2nd hyper Gourava index, Product connectivity Gourava index, Sum connectivity Gourava index, Forgotten index, Forgotten polynomials, M-polynomials and some topological indices in term of the M-polynomials i.e. 1st Zagreb index, 2nd Zagreb index, Modified 2nd Zagreb, Randi´c index, Reciprocal Randi´c index, Symmetric division, Harmonic index, Inverse Sum index, Augmented Zagreb index for the semitotal-point graph and line graph of semitotal-point graph for Dutch windmill graph.

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Analysis of COVID-19 by Means of Graph Theory

Scientific Inquiry and Review ◽

10.32350/sir.42.04 ◽

2020 ◽

Vol 4 (2) ◽

pp. 48-62

Author(s):

Abaid ur Rehman Virik ◽

Iqra Malik

Keyword(s):

Biological Activity ◽

Graph Theory ◽

Topological Index ◽

General Type ◽

Randić Index ◽

Zagreb Index ◽

Randic Index ◽

Zagreb Indices ◽

Augmented Zagreb Index ◽

Modified Zagreb Index

As a powerful displaying, investigation and computational device, graph theory is widely used in biological mathematics to deal with various biology problems. In the field of microbiology, graphs can communicate the sub-atomic structure. Where cell, quality or protein can be indicated as a vertex, and the associate component can be viewed as an edge. Thusly, the biological activity characteristic can be measured via topological index computing in the comparing graphs. In this article, we for the most part concentrate some topological lists for the Corona virus graph. At first,we give a general type of M-polynomial. From the M-polynomial, we recoup some well-known degree-based topological lists, for example, First and Second Zagreb Indices, Second Modified Zagreb Index, Randic´ Index, General Randic´ Index, Symmetric Division Index, Harmonic Index, Inverse Sum Index, Augmented Zagreb Index. Our results are extensions of many existing results.

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On Leap Reduced Reciprocal Randic and Leap Reduced Second Zagreb Indices of Some Graphs

Scientific Inquiry and Review ◽

10.32350/sir.32.04 ◽

2019 ◽

Vol 3 (2) ◽

pp. 27-35

Author(s):

Fazal Dayan ◽

Muhammad Javaid ◽

Muhammad Aziz ur Rehman

Keyword(s):

Topological Indices ◽

Randić Index ◽

Zagreb Index ◽

Randic Index ◽

Zagreb Indices ◽

Second Zagreb Index ◽

Second Degree

Naji et al. introduced the leap Zagreb indices of a graph in 2017 which are new distance-degree-based topological indices conceived depending on the second degree of vertices. In this paper, we have defined the first and second leap reduced reciprocal Randic index and leap reduced second Zagreb index for selected wheel related graphs.

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Topology-Based Analysis of OTIS (Swapped) Networks OKn and OPn

Journal of Chemistry ◽

10.1155/2019/4291943 ◽

2019 ◽

Vol 2019 ◽

pp. 1-11

Author(s):

Hai-Xia Li ◽

Sarfaraz Ahmad ◽

Iftikhar Ahmad

Keyword(s):

Topological Index ◽

Molecular Descriptor ◽

Randić Index ◽

Zagreb Index ◽

Randic Index ◽

Chemical Graph ◽

Zagreb Indices ◽

Second Zagreb Index ◽

Chemical Graph Theory ◽

Augmented Zagreb Index

In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound. In this paper, M-polynomial OKn and OPn networks are computed. The M-polynomial is rich in information about degree-based topological indices. By applying the basic rules of calculus on M-polynomials, the first and second Zagreb indices, modified second Zagreb index, general Randić index, inverse Randić index, symmetric division index, harmonic index, inverse sum index, and augmented Zagreb index are recovered.

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On Analysis of Topological Aspects for Subdivision of Kragujevac Tree Networks

Mathematical Problems in Engineering ◽

10.1155/2021/9082320 ◽

2021 ◽

Vol 2021 ◽

pp. 1-15

Author(s):

Salma Kanwal ◽

Shanshan Shang ◽

Muhammad Kamran Siddiqui ◽

Tahira Sumbal Shaikh ◽

Ammara Afzal ◽

...

Keyword(s):

Line Graph ◽

Topological Indices ◽

Zagreb Index ◽

Tree Networks ◽

Harmonic Index ◽

Symmetric Division ◽

Second Zagreb Index ◽

Augmented Zagreb Index ◽

Forgotten Index ◽

Topological Characteristics

In this paper, we have taken review of certain topological topological characteristics of subdivision and the line graph of subdivision of Kragujevac tree. A Kragujevac tree is denoted by K , K ∈ Kg q = r 2 t + 1 + 1 , r , with order r 2 t + 1 + 1 and size r 2 t + 1 , respectively. We have computed the Zagreb polynomials, forgotten polynomial, and M-polynomial for Kragujevac tree. Moreover, we have computed topological indices like Zagreb-type indices, reduced reciprocal Randić indices, family of Gourava indices as well as forgotten index. Further, some topological indices that can be directly derived from M-polynomial, i.e., first and second Zagreb index, modified second Zagreb index, Randić and reciprocal Randić index, symmetric division and harmonic index, and inverse sum and augmented Zagreb index are also computed.

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Topological Indices of Certain Transformed Chemical Structures

Journal of Chemistry ◽

10.1155/2020/3045646 ◽

2020 ◽

Vol 2020 ◽

pp. 1-7 ◽

Cited By ~ 1

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.

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Several Topological Indices of Two Kinds of Tetrahedral Networks

Journal of Mathematics ◽

10.1155/2021/9800246 ◽

2021 ◽

Vol 2021 ◽

pp. 1-10

Author(s):

Jia-Bao Liu ◽

Lu-Lu Fang

Keyword(s):

Finite Element ◽

Network Model ◽

Topological Indices ◽

Randić Index ◽

Zagreb Index ◽

Randic Index ◽

Research Studies

Tetrahedral network is considered as an effective tool to create the finite element network model of simulation, and many research studies have been investigated. The aim of this paper is to calculate several topological indices of the linear and circle tetrahedral networks. Firstly, the resistance distances of the linear tetrahedral network under different classifications have been calculated. Secondly, according to the above results, two kinds of degree-Kirchhoff indices of the linear tetrahedral network have been achieved. Finally, the exact expressions of Kemeny’s constant, Randic index, and Zagreb index of the linear tetrahedral network have been deduced. By using the same method, the topological indices of circle tetrahedral network have also been obtained.

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M-polynomial and topological indices of some transformed networks

AIMS Mathematics ◽

10.3934/math.2021804 ◽

2021 ◽

Vol 6 (12) ◽

pp. 13887-13906

Author(s):

Fei Yu ◽

◽

Hifza Iqbal ◽

Saira Munir ◽

Jia Bao Liu ◽

...

Keyword(s):

Interconnection Networks ◽

Chemical Compounds ◽

Topological Indices ◽

Randić Index ◽

Topological Properties ◽

Randic Index ◽

Zagreb Indices ◽

General Randić Index ◽

General Randic Index ◽

Dual Operations

<abstract>In the chemical industry, topological indices play an important role in defining the properties of chemical compounds. They are numerical parameters and structure invariant. It is a proven fact by scientists that topological properties are influential tools for interconnection networks. In this paper, we will use stellation, medial and bounded dual operations to build transformed networks from zigzag and triangular benzenoid structures. Using M-polynomial, we compute the first and second Zagreb indices, second modified Zagreb indices, symmetric division index, general Randic index, reciprocal general Randic index. We also calculate atomic bond connectivity index, geometric arithmetic index, harmonic index, first and second Gourava indices, first and second hyper Gourava indices.</abstract>

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Computing Zagreb and Randić Indices of PEG-Cored Dendrimers Used for Drug and Gene Delivery

Journal of Chemistry ◽

10.1155/2020/2821510 ◽

2020 ◽

Vol 2020 ◽

pp. 1-7

Author(s):

Thayamathy Pio Jude ◽

Elango Panchadcharam ◽

Koneswaran Masilamani

Keyword(s):

Gene Delivery ◽

Drug Design ◽

Topological Indices ◽

Randić Index ◽

Molecular Topology ◽

Design And Development ◽

Randic Index ◽

Zagreb Indices ◽

Chemical Structures ◽

Drug And Gene Delivery

Zagreb and Randić indices are the most commonly used degree-based topological indices in the study of drug design and development. In molecular topology, M-polynomials are also used to calculate the degree-based topological indices of chemical structures. In this paper, we derive the M-polynomials for the PEG-cored PAMAM, carbosilane, and poly (lysine) dendrimers and calculate their first, second, and second modified Zagreb indices and the Randić index.

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Topological Indices of Dendrimers used in Drug Delivery

Journal of Scientific Research ◽

10.3329/jsr.v12i4.45389 ◽

2020 ◽

Vol 12 (4) ◽

pp. 645-655

Author(s):

T. P. Jude ◽

E. Panchadcharam ◽

K. Masilamani

Keyword(s):

Drug Delivery ◽

Molecular Graph ◽

Topological Indices ◽

Vertex Degree ◽

Numerical Representation ◽

Chemical Bonds ◽

Randić Index ◽

Zagreb Index ◽

Randic Index ◽

Carrier Vehicle

The topological index is a numerical representation of a molecular structure. In chemical graphs, the atoms and the chemical bonds between them are represented by vertices and edges respectively. Vertex degree based topological indices are the most studied and mostly used type of topological indices. The mostly used vertex degree based topological indices in the field of drug design and developments are the Zagreb index and the Randić index. The structural chemistry of dendrimers could be manipulated by their topological indices to get the specific structure with required properties to deliver the drugs to target carrier vehicle. In this work, topological indices of three types of dendrimers which are used as the drug delivery system were studied and their Zagreb index and the Randić index were calculated using molecular graph theory. Moreover, the other versions of these two indices were also calculated to these dendrimers.

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