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.

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 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.

Some topological indices of dendrimers

2020 ◽  
pp. 2050018
Author(s):  
S. Alyar ◽  
R. Khoeilar ◽  
A. Jahanbani
Keyword(s):  
Graph Theory ◽  
Molecular Graph ◽  
Topological Indices ◽  
Molecular Structures ◽  
Topological Properties ◽  
Zagreb Index ◽  
Zinc Porphyrin ◽  
Molecular Graphs

There are immense applications of graph theory in chemistry and in the study of molecular structures, and after that, it has been increasing exponentially. Molecular graphs have points (vertices) representing atoms and lines (edges) that represent bonds between atoms. In this paper, we study the molecular graph of porphyrin, propyl ether imine, zinc–porphyrin and poly dendrimers and analyzed its topological properties. For this purpose, we have computed topological indices, namely the Albertson index, the sigma index, the Nano-Zagreb index, the first and second hyper [Formula: see text]-indices of porphyrin, propyl ether imine, zinc–porphyrin and poly dendrimers.

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 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 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 Modified Zagreb connection indices of the T-sum graphs

2020 ◽  
Vol 43 (1) ◽  
pp. 43-55 ◽  
Author(s):  
Usman Ali ◽  
Muhammad Javaid ◽  
Agha Kashif
Keyword(s):  
Molecular Graph ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Line Graphs ◽  
Real Numbers ◽  
Statistical Tools ◽  
Zagreb Indices ◽  
Molecular Graphs ◽  
Octane Isomers

AbstractThe quantitative structures activity relationships (QSAR) and quantitative structures property relationships (QSPR) between the chemical compounds are studied with the help of topological indices (TI’s) which are the fixed real numbers directly linked with the molecular graphs. Gutman and Trinajstic (1972) defined the first degree based TI to measure the total π-electrone energy of a molecular graph. Recently, Ali and Trinajstic (2018) restudied the connection based TI’s such as first Zagreb connection index, second Zagreb connection index and modified first Zagreb connection index to find entropy and accentric factor of the octane isomers. In this paper, we study the modified second Zagreb connection index and modified third Zagreb connection index on the T-sum (molecular) graphs obtained by the operations of subdivision and product on two graphs. At the end, as the applications of the obtained results for the modified Zagreb connection indices of the T-sum graphs of the particular classes of alkanes are also included. Mainly, a comparision among the Zagreb indices, Zagreb connection indices and modified Zagreb connection indices of the T-sum graphs of the particular classes of alkanes is performed with the help of numerical tables, 3D plots and line graphs using the statistical tools.

WEIGHTED MOSTAR INDICES OF CERTAIN GRAPHS

2021 ◽  
Vol 10 (9) ◽  
pp. 3093-3111
Author(s):  
P. Kandan ◽  
S. Subramanian ◽  
P. Rajesh
Keyword(s):  
Graph Theory ◽  
Chemical Compound ◽  
Molecular Graph ◽  
Topological Indices ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
And Mathematics

Chemical graph theory is a mixture of chemistry and mathematics both play an important role in chemical graph theory. Chemistry provides a chemical compound and graph theory transform this chemical compound into a molecular graph, which are associated with some numerical values these values are known as topological indices. In this study we consider the weighted modification of new bond-additive Mostar indices that appear to provide quantitative measures of peripheral shapes of molecules. We have computed the Additively Weighted Mostar Index and Multiplicatively Weighted Mostar Index for Conical and Generalized gear graph.

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.

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