scholarly journals M-Polynomials and Topological Indices for Line Graphs of Chain Silicate Network and H-Naphtalenic Nanotubes

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Muhammad Irfan ◽  
Hamood Ur Rehman ◽  
Hassan Almusawa ◽  
Saffina Rasheed ◽  
Imran Abbas Baloch
Keyword(s):  
Graph Theory ◽  
Topological Index ◽  
Chemical Properties ◽  
Topological Indices ◽  
Line Graphs ◽  
Silicate Network ◽  
Chemical Graph ◽  
Chain Silicate

Graph theory has provided a very useful tool, called topological index, which is a number from the graph M with the property that every graph N isomorphic to M value of a topological index must be same for both M and N. Topological index is a descriptor in graph theory which is used to quantify the physio-chemical properties of the chemical graph. In this paper, we computed closed forms of M-polynomials for line graphs of H-naphtalenic nanotubes and chain silicate network. From M-polynomial, we obtained some topological indices based on degrees.

scholarly journals Computation of Nirmala Indices of Some Chemical Networks

2021 ◽  
Vol 33 (4) ◽  
pp. 30-41
Author(s):  
V.R. KULLI ◽  
◽  
B. CHALUVARAJU ◽  
T.V. ASHA ◽  
◽  
...  
Keyword(s):  
Graph Theory ◽  
Comparative Analysis ◽  
Chemical Properties ◽  
Topological Indices ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Chemical Graphs ◽  
Chain Silicate

Chemical graph theory is a branch of graph theory whose focus of interest is to finding topological indices of chemical graphs which correlate well with chemical properties of the chemical molecules. In this paper, we compute the Nirmala index, first and second inverse Nirmala indices for some chemical networks like silicate networks, chain silicate networks, hexagonal networks, oxide networks and honeycomb networks along with their comparative analysis.

scholarly journals Degree-Based Indices of Some Complex Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Lei Ding ◽  
Syed Ahtsham Ul Haq Bokhary ◽  
Masood Ur Rehman ◽  
Usman Ali ◽  
Hirra Mubeen ◽  
...  
Keyword(s):  
Graph Theory ◽  
Complex Networks ◽  
Topological Index ◽  
Chemical Properties ◽  
Topological Indices ◽  
Mesh Network ◽  
Silicate Network ◽  
Physico Chemical ◽  
Rhenium Trioxide ◽  
Atom Bond

A topological index is a numeric quantity assigned to a graph that characterizes the structure of a graph. Topological indices and physico-chemical properties such as atom-bond connectivity ABC , Randić, and geometric-arithmetic index GA are of great importance in the QSAR/QSPR analysis and are used to estimate the networks. In this area of research, graph theory has been found of considerable use. In this paper, the distinct degrees and degree sums of enhanced Mesh network, triangular Mesh network, star of silicate network, and rhenium trioxide lattice are listed. The edge partitions of these families of networks are tabled which depend on the sum of degrees of end vertices and the sum of the degree-based edges. Utilizing these edge partitions, the closed formulae for some degree-based topological indices of the networks are deduced.

scholarly journals M-polynomial and topological indices of zigzag edge coronoid fused by starphene

2020 ◽  
Vol 18 (1) ◽  
pp. 1362-1369
Author(s):  
Farkhanda Afzal ◽  
Sabir Hussain ◽  
Deeba Afzal ◽  
Saira Hameed
Keyword(s):  
Graph Theory ◽  
Chemical Properties ◽  
Topological Indices ◽  
Zigzag Edge ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Chemical Graphs

AbstractChemical graph theory is a subfield of graph theory that studies the topological indices for chemical graphs that have a good correlation with chemical properties of a chemical molecule. In this study, we have computed M-polynomial of zigzag edge coronoid fused by starphene. We also investigate various topological indices related to this graph by using their M-polynomial.

scholarly journals Computing Some Degree-Based Topological Indices of Honeycomb Networks

Complexity ◽  
2022 ◽  
Vol 2022 ◽  
pp. 1-13
Author(s):  
Lili Gu ◽  
Shamaila Yousaf ◽  
Akhlaq Ahmad Bhatti ◽  
Peng Xu ◽  
Adnan Aslam
Keyword(s):  
Chemical Structure ◽  
Chemical Properties ◽  
Chemical Substance ◽  
Topological Indices ◽  
Connectivity Index ◽  
Silicate Network ◽  
Zagreb Index ◽  
First Order ◽  
Second Zagreb Index ◽  
Chain Silicate

A topological index is a numeric quantity related with the chemical composition claiming to correlate the chemical structure with different chemical properties. Topological indices serve to predict physicochemical properties of chemical substance. Among different topological indices, degree-based topological indices would be helpful in investigating the anti-inflammatory activities of certain chemical networks. In the current study, we determine the neighborhood second Zagreb index and the first extended first-order connectivity index for oxide network O X n , silicate network S L n , chain silicate network C S n , and hexagonal network H X n . Also, we determine the neighborhood second Zagreb index and the first extended first-order connectivity index for honeycomb network H C n .

scholarly journals Topological study of the para-line graphs of certain pentacene via topological indices

2018 ◽  
Vol 16 (1) ◽  
pp. 1200-1206 ◽  
Author(s):  
Zeeshan Saleem Mufti ◽  
Muhammad Faisal Nadeem ◽  
Wei Gao ◽  
Zaheer Ahmad
Keyword(s):  
Molecular Structure ◽  
Real Number ◽  
Chemical Structure ◽  
Topological Index ◽  
Line Graph ◽  
Chemical Properties ◽  
Topological Indices ◽  
Molecular Structures ◽  
Line Graphs ◽  
Graph Invariant

AbstractA topological index is a map from molecular structure to a real number. It is a graph invariant and also used to describe the physio-chemical properties of the molecular structures of certain compounds. In this paper, we have investigated a chemical structure of pentacene. Our paper reflects the work on the following indices:Rα, Mα, χα, ABC, GA, ABC4, GA5, PM1, PM2, M1(G, p)and M1(G, p) of the para-line graph of linear [n]-pentacene and multiple pentacene.

scholarly journals Banhatti, revan and hyper-indices of silicon carbide Si2C3-III[n,m]

2021 ◽  
Vol 19 (1) ◽  
pp. 646-652
Author(s):  
Dongming Zhao ◽  
Manzoor Ahmad Zahid ◽  
Rida Irfan ◽  
Misbah Arshad ◽  
Asfand Fahad ◽  
...  
Keyword(s):  
Silicon Carbide ◽  
Graph Theory ◽  
Topological Index ◽  
Molecular Graph ◽  
Graphical Analysis ◽  
Topological Indices ◽  
Chemical Bonds ◽  
Chemical Graph ◽  
Molecular Graphs ◽  
Chemical Graph Theory

Abstract In recent years, several structure-based properties of the molecular graphs are understood through the chemical graph theory. The molecular graph G G of a molecule consists of vertices and edges, where vertices represent the atoms in a molecule and edges represent the chemical bonds between these atoms. A numerical quantity that gives information related to the topology of the molecular graphs is called a topological index. Several topological indices, contributing to chemical graph theory, have been defined and vastly studied. Recent inclusions in the class of the topological indices are the K-Banhatti indices. In this paper, we established the precise formulas for the first and second K-Banhatti, modified K-Banhatti, K-hyper Banhatti, and hyper Revan indices of silicon carbide Si 2 C 3 {{\rm{Si}}}_{2}{{\rm{C}}}_{3} - III [ n , m ] {\rm{III}}\left[n,m] . In addition, we present the graphical analysis along with the comparison of these indices for Si 2 C 3 {{\rm{Si}}}_{2}{{\rm{C}}}_{3} - III [ n , m ] {\rm{III}}\left[n,m] .

scholarly journals Some degree-based topological indices of caboxy-terminated dendritic macromolecule

2021 ◽  
Vol 44 (1) ◽  
pp. 165-172
Author(s):  
Yongsheng Rao ◽  
Ammarah Kanwal ◽  
Riffat Abbas ◽  
Saima Noureen ◽  
Asfand Fahad ◽  
...  
Keyword(s):  
Graph Theory ◽  
Chemical Properties ◽  
Biochemical Properties ◽  
Topological Indices ◽  
Connectivity Index ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Modern Era ◽  
Dendritic Macromolecule ◽  
Atom Bond

Abstract In the modern era of the chemical science, the chemical graph theory has contributed significantly to exploring the properties of the chemical compounds. Currently, the computation of the topological indices is one of the most active directions of the research in the area of the chemical graph theory. The main feature of the study of the topological indices is its its ability of predicting the various physio-chemical properties. In this article, we compute several degree-based topological indices for the caboxy-terminated dendritic macromolecule. We compute Harmonic index, atom-bond connectivity index, geometric arithmetic index, sum connectivity index, inverse sum index, symmetric division degree, and Zagreb indices for caboxy-terminated dendritic macromolecule. The obtained results have potential to predict biochemical properties such as viscosity, entropy, and boiling point.

scholarly journals Multiplicative topological indices of honeycomb derived networks

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 16-30
Author(s):  
Jiang-Hua Tang ◽  
Mustafa Habib ◽  
Muhammad Younas ◽  
Muhammad Yousaf ◽  
Waqas Nazeer
Keyword(s):  
Graph Theory ◽  
Structural Properties ◽  
Chemical Properties ◽  
Vital Role ◽  
Topological Indices ◽  
Chemical Graph ◽  
Chemical Structures ◽  
Chemical Graph Theory ◽  
Physico Chemical

Abstract Topological indices are the numerical values associated with chemical structures that correlate physico-chemical properties with structural properties. There are various classes of topological indices such as degree based topological indices, distance based topological indices and counting related topological indices. Among these classes, degree based topological indices are of great importance and play a vital role in chemical graph theory, particularly in chemistry. In this report, we have computed the multiplicative degree based topological indices of honeycomb derived networks of dimensions I, 2, 3 and 4.

scholarly journals On Distance-Based Topological Descriptors of Chemical Interconnection Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Min Hu ◽  
Haidar Ali ◽  
Muhammad Ahsan Binyamin ◽  
Bilal Ali ◽  
Jia-Bao Liu ◽  
...  
Keyword(s):  
Interconnection Networks ◽  
Topological Index ◽  
Chemical Properties ◽  
Topological Descriptors ◽  
Silicate Network ◽  
Pi Index ◽  
Szeged Index ◽  
Physico Chemical ◽  
Chain Silicate ◽  
First Time

Structure-based topological descriptors of chemical networks enable us the prediction of physico-chemical properties and the bioactivities of compounds through QSAR/QSPR methods. Topological indices are the numerical values to represent a graph which characterises the graph. One of the latest distance-based topological index is the Mostar index. In this paper, we study the Mostar index, Szeged index, PI index, ABC GG index, and NGG index, for chain oxide network COX n , chain silicate network CS n , ortho chain S n , and para chain Q n , for the first time. Moreover, analytically closed formulae for these structures are determined.

scholarly journals Computing Topological Indices for Para-Line Graphs of Anthracene

2019 ◽  
Vol 17 (1) ◽  
pp. 955-962 ◽  
Author(s):  
Zhiqiang Zhang ◽  
Zeshan Saleem Mufti ◽  
Muhammad Faisal Nadeem ◽  
Zaheer Ahmad ◽  
Muhammad Kamran Siddiqui ◽  
...  
Keyword(s):  
Graph Theory ◽  
Chemical Compound ◽  
Line Graph ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Molar Refraction ◽  
Chromatographic Behavior ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
And Mathematics

AbstractAtoms displayed as vertices and bonds can be shown by edges on a molecular graph. For such graphs we can find the indices showing their bioactivity as well as their physio-chemical properties such as the molar refraction, molar volume, chromatographic behavior, heat of atomization, heat of vaporization, magnetic susceptibility, and the partition coefficient. Today, industry is flourishing because of the interdisciplinary study of different disciplines. This provides a way to understand the application of different disciplines. Chemical graph theory is a mixture of chemistry and mathematics, which plays an important role in chemical graph theory. Chemistry provides a chemical compound, and graph theory transforms this chemical compound into a molecular graphwhich further is studied by different aspects such as topological indices.We will investigate some indices of the line graph of the subdivided graph (para-line graph) of linear-[s] Anthracene and multiple Anthracene.

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