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

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.

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

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.

Four New/Old Vertex-Degree-Based Topological Indices of HAC5C7[p, q] and HAC5C6C7[p, q] Nanotubes

2017 ◽  
Vol 14 (1) ◽  
pp. 796-799 ◽  
Author(s):  
Yingfang Li ◽  
Li Yan ◽  
Muhammad Kamran Jamil ◽  
Mohammad Reza Farahani ◽  
Wei Gao ◽  
...  
Keyword(s):  
Topological Indices ◽  
Vertex Degree ◽  
Randić Index ◽  
Zagreb Index ◽  
Randic Index ◽  
Second Zagreb Index ◽  
Forgotten Index ◽  
Mathematical Literature

Recently, Gutman et al. presented some vertex-degree based topological indices, that earlier have been considered in the chemical and/or mathematical literature, but, evaded the attention of most mathematical chemists. These are the reciprocal Randic index (RR), the reduced reciprocal Randic index (RRR), the reduced second Zagreb index (RM2) and the forgotten index (F). In this paper, we compute these topological indices of HAC5C7[p, q] and HAC5C6C7[p, q] nanotubes.

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

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Faryal Chaudhry ◽  
Iqra Shoukat ◽  
Deeba Afzal ◽  
Choonkil Park ◽  
Murat Cancan ◽  
...  
Keyword(s):  
Topological Indices ◽  
Randić Index ◽  
Zagreb Index ◽  
Harmonic Index ◽  
Randic Index ◽  
Zagreb Indices ◽  
Symmetric Division ◽  
Augmented Zagreb Index ◽  
Physical And Chemical ◽  
Modified Zagreb Index

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.

scholarly journals Several Topological Indices of Two Kinds of Tetrahedral Networks

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.

scholarly journals M-polynomial and topological indices of some transformed networks

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><p>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.</p></abstract>

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.

Tetracyclic graphs with maximum second Zagreb index: A simple approach

2018 ◽  
Vol 11 (05) ◽  
pp. 1850064 ◽  
Author(s):  
Akbar Ali
Keyword(s):  
Graph Theory ◽  
Short Note ◽  
Topological Indices ◽  
Simple Approach ◽  
Graph Invariants ◽  
Zagreb Index ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Second Zagreb Index ◽  
Chemical Graph Theory

In the chemical graph theory, graph invariants are usually referred to as topological indices. The second Zagreb index (denoted by [Formula: see text]) is one of the most studied topological indices. For [Formula: see text], let [Formula: see text] be the collection of all non-isomorphic connected graphs with [Formula: see text] vertices and [Formula: see text] edges (such graphs are known as tetracyclic graphs). Recently, Habibi et al. [Extremal tetracyclic graphs with respect to the first and second Zagreb indices, Trans. on Combin. 5(4) (2016) 35–55.] characterized the graph having maximum [Formula: see text] value among all members of the collection [Formula: see text]. In this short note, an alternative but relatively simple approach is used for characterizing the aforementioned graph.

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

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.

scholarly journals First and Second Zagreb Polynomials of VC5C7[p,q] and HC5C7[p,q]Nanotubes

2014 ◽  
Vol 31 ◽  
pp. 56-62 ◽  
Author(s):  
Mohammad Reza Farahani
Keyword(s):  
Graph Theory ◽  
Connected Graph ◽  
Topological Indices ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Second Zagreb Index ◽  
Connectivity Indices ◽  
Anti Inflammatory ◽  
Simple Connected Graph

Let G = (V,E) be a simple connected graph. The sets of vertices and edges of G are denoted by V = V(G) and E = E(G), respectively. There exist many topological indices and connectivity indices in graph theory. The First and Second Zagreb indices were first introduced by Gutman and Trinajstić In1972. It is reported that these indices are useful in the study of anti-inflammatory activities of certain chemical instances, and in elsewhere. In this paper, we focus on the structure of ”G = VC5C7[p,q]”and ”H = HC5C7[p,q]” nanotubes and counting first Zagreb index Zg1(G) = ∑veVdv2 and Second Zagreb index Zg2(G) =∑e=uveE(G)(du·dv) of G and H, as well as First Zagreb polynomial Zg1(G,x ) =∑e=uveE(G)xdu+dv and Second Zagreb Polynomial Zg2(G,x) = ∑e=uveE(G)xdu·dv

scholarly journals Topological Indices of Dendrimers used in Drug Delivery

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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