scholarly journals A Comparison Study of Irregularity Descriptors of Benzene Ring Embedded in P-Type Surface Network and Its Derived Network

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Nehad Ali Shah
Keyword(s):  
Benzene Ring ◽  
Line Graph ◽  
Quantitative Structure Activity Relationship ◽  
Quantitative Structure ◽  
Structure Property ◽  
Graphical Comparison ◽  
Structure Property Relationship ◽  
Surface Network ◽  
Breaking Points ◽  
P Type

Topological indices are atomic auxiliary descriptors which computationally and hypothetically portray the natures of the basic availability of nanomaterials and chemical mixes, and henceforth, they give faster techniques to look at their exercises and properties. Anomaly indices are for the most part used to describe the topological structures of unpredictable graphs. Graph anomaly examines are helpful not only for quantitative structure-activity relationship (QSAR) and also quantitative structure-property relationship (QSPR) but also for foreseeing their different physical and compound properties, including poisonousness, obstruction, softening and breaking points, the enthalpy of vanishing, and entropy. In this article, we discuss the irregularities of benzene ring and its line graph and compare them by its irregularity indices. We present graphical comparison by using Mathematica.

scholarly journals Topological indices of rhombus type silicate and oxide networks

2017 ◽  
Vol 95 (2) ◽  
pp. 134-143 ◽  
Author(s):  
M. Javaid ◽  
Masood Ur Rehman ◽  
Jinde Cao
Keyword(s):  
Molecular Graph ◽  
Chemical Compounds ◽  
Quantitative Structure Activity Relationship ◽  
Topological Indices ◽  
Quantitative Structure ◽  
Structure Property ◽  
Structure Activity ◽  
Structure Property Relationship ◽  
Cartesian Coordinate ◽  
Atom Bond

For a molecular graph, a numeric quantity that characterizes the whole structure of a graph is called a topological index. In the studies of quantitative structure – activity relationship (QSAR) and quantitative structure – property relationship (QSPR), topological indices are utilized to guess the bioactivity of chemical compounds. In this paper, we compute general Randić, first general Zagreb, generalized Zagreb, multiplicative Zagreb, atom-bond connectivity (ABC), and geometric arithmetic (GA) indices for the rhombus silicate and rhombus oxide networks. In addition, we also compute the latest developed topological indices such as the fourth version of ABC (ABC4), the fifth version of GA (GA5), augmented Zagreb, and Sanskruti indices for the foresaid networks. At the end, a comparison between all the indices is included, and the result is shown with the help of a Cartesian coordinate system.

scholarly journals The General Connectivity and General Sum-Connectivity Indices of Nanostructures

2015 ◽  
Vol 44 ◽  
pp. 73-80
Author(s):  
Mohammad Reza Farahani
Keyword(s):  
Quantitative Structure Activity Relationship ◽  
Connectivity Index ◽  
Quantitative Structure ◽  
Structure Property ◽  
The Third ◽  
Structure Activity ◽  
New Variant ◽  
Connectivity Indices ◽  
Structure Property Relationship ◽  
Vertex Set

Let G be a simple graph with vertex set V(G) and edge set E(G). For ∀νi∈V(G),di denotes the degree of νi in G. The Randić connectivity index of the graph G is defined as [1-3] χ(G)=∑e=v1v2є(G)(d1d2)-1/2. The sum-connectivity index is defined as χ(G)=∑e=v1v2є(G)(d1+d2)-1/2. The sum-connectivity index is a new variant of the famous Randić connectivity index usable in quantitative structure-property relationship and quantitative structure-activity relationship studies. The general m-connectivety and general m-sum connectivity indices of G are defined as mχ(G)=∑e=v1v2...vim+1(1/√(di1di2...dim+1)) and mχ(G)=∑e=v1v2...vim+1(1/√(di1+di2+...+dim+1)) where vi1vi2...vim+1 runs over all paths of length m in G. In this paper, we introduce a closed formula of the third-connectivity index and third-sum-connectivity index of nanostructure "Armchair Polyhex Nanotubes TUAC6[m,n]" (m,n≥1).

scholarly journals On Knowledge Discovery and Representations of Molecular Structures Using Topological Indices

2021 ◽  
Vol 11 (1) ◽  
pp. 21-32
Author(s):  
Fawaz E. Alsaadi ◽  
Syed Ahtsham Ul Haq Bokhary ◽  
Aqsa Shah ◽  
Usman Ali ◽  
Jinde Cao ◽  
...  
Keyword(s):  
Topological Index ◽  
Chemical Compounds ◽  
Quantitative Structure Activity Relationship ◽  
Topological Indices ◽  
Molecular Structures ◽  
Quantitative Structure ◽  
Structure Property ◽  
Graph Automorphism ◽  
Structure Property Relationship ◽  
Atom Bond

AbstractThe main purpose of a topological index is to encode a chemical structure by a number. A topological index is a graph invariant, which decribes the topology of the graph and remains constant under a graph automorphism. Topological indices play a wide role in the study of QSAR (quantitative structure-activity relationship) and QSPR (quantitative structure-property relationship). Topological indices are implemented to judge the bioactivity of chemical compounds. In this article, we compute the ABC (atom-bond connectivity); ABC4 (fourth version of ABC), GA (geometric arithmetic) and GA5 (fifth version of GA) indices of some networks sheet. These networks include: octonano window sheet; equilateral triangular tetra sheet; rectangular sheet; and rectangular tetra sheet networks.

scholarly journals Bounds for the Topological Indices of ℘ graph

2021 ◽  
Vol 14 (2) ◽  
pp. 340-350
Author(s):  
Muddalapuram Manjunath ◽  
V. Lokesha ◽  
. Suvarna ◽  
Sushmitha Jain
Keyword(s):  
Finite Graph ◽  
Quantitative Structure Activity Relationship ◽  
Topological Indices ◽  
Quantitative Structure ◽  
Structure Property ◽  
Lower And Upper Bounds ◽  
Zagreb Index ◽  
Chemical Structures ◽  
Structure Property Relationship ◽  
Atom Bond

Topological indices are mathematical measure which correlates to the chemical structures of any simple finite graph. These are used for Quantitative Structure-Activity Relationship (QSAR) and Quantitative Structure-Property Relationship (QSPR). In this paper, we define operator graph namely, ℘ graph and structured properties. Also, establish the lower and upper bounds for few topological indices namely, Inverse sum indeg index, Geometric-Arithmetic index, Atom-bond connectivity index, first zagreb index and first reformulated Zagreb index of ℘-graph.

scholarly journals Computation of certain topological coindices of graphene sheet and C4C8(S) nanotubes and nanotorus

2019 ◽  
Vol 4 (2) ◽  
pp. 455-468 ◽  
Author(s):  
Melaku Berhe ◽  
Chunxiang Wang
Keyword(s):  
Graphene Sheet ◽  
Biological Activities ◽  
Chemical Properties ◽  
Quantitative Structure Activity Relationship ◽  
Topological Indices ◽  
Quantitative Structure ◽  
Structure Property ◽  
Structure Property Relationship ◽  
Relationship Of ◽  
The Relationship

AbstractTopological indices are widely used for quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR). Topological coindices are topological indices that considers the non adjacent pairs of vertices. Here, we consider the following five well-known topological coindices: the first and second Zagreb coindices, the first and second multiplicative Zagreb coindices and the F-coindex. By using graph structural analysis and derivation, we study the above-mentioned topological coindices of some chemical molecular graphs that frequently appear in medical, chemical, and material engineering such as graphene sheet and C4C8(S) nanotubes and nanotorus and obtain the computation formulae of the coindices of these graphs. Furthermore, we analyze the results by MATLAB and obtain the relationship of the coindices which they describe the physcio-chemical properties and biological activities.

scholarly journals On Degree Based Topological Indices of TiO2 Crystal via M-Polynomial

2022 ◽  
Vol 19 (2) ◽  
pp. 2022
Author(s):  
Tapan Kumar Baishya ◽  
Bijit Bora ◽  
Pawan Chetri ◽  
Upashana Gogoi
Keyword(s):  
Molecular Graph ◽  
Quantitative Structure Activity Relationship ◽  
Topological Indices ◽  
Three Dimensions ◽  
Topological Descriptors ◽  
Quantitative Structure ◽  
Structure Property ◽  
Physiochemical Properties ◽  
3 Dimensional ◽  
Structure Property Relationship

Topological indices (TI) (descriptors) of a molecular graph are very much useful to study various physiochemical properties. It is also used to develop the quantitative structure-activity relationship (QSAR), quantitative structure-property relationship (QSPR) of the corresponding chemical compound. Various techniques have been developed to calculate the TI of a graph. Recently a technique of calculating degree-based TI from M-polynomial has been introduced. We have evaluated various topological descriptors for 3-dimensional TiO2 crystals using M-polynomial. These descriptors are constructed such that it contains 3 variables (m, n and t) each corresponding to a particular direction. These 3 variables facilitate us to deeply understand the growth of TiO2 in 1 dimension (1D), 2 dimensions (2D), and 3 dimensions (3D) respectively. HIGHLIGHTS Calculated degree based Topological indices of a 3D crystal from M-polynomial A relation among various Topological indices is established geometrically Variations of Topological Indices along three dimensions (directions) are shown geometrically Harmonic index approximates the degree variation of oxygen atom

scholarly journals A quantitative structure–property study of reorganization energy for known p-type organic semiconductors

RSC Advances ◽  
2018 ◽  
Vol 8 (70) ◽  
pp. 40330-40337 ◽  
Author(s):  
Sule Atahan-Evrenk
Keyword(s):  
Molecular Structure ◽  
Organic Semiconductors ◽  
Reorganization Energy ◽  
Quantitative Structure ◽  
Structure Property ◽  
Property Relationship ◽  
Structure Property Relationship ◽  
P Type

An investigation of the structure–property relationship between reorganization energy and molecular structure.

scholarly journals Minimum Detour Index of Tricyclic Graphs

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Wei Fang ◽  
Zheng-Qun Cai ◽  
Xiao-Xin Li
Keyword(s):  
Connected Graph ◽  
Quantitative Structure Activity Relationship ◽  
Activity Relationship ◽  
Quantitative Structure ◽  
Structure Property ◽  
Quantitative Structure Property Relationship ◽  
Structure Activity ◽  
Structure Property Relationship ◽  
Longest Paths ◽  
Tricyclic Graphs

The detour index of a connected graph is defined as the sum of the detour distances (lengths of longest paths) between unordered pairs of vertices of the graph. The detour index is used in various quantitative structure-property relationship and quantitative structure-activity relationship studies. In this paper, we characterize the minimum detour index among all tricyclic graphs, which attain the bounds.

scholarly journals An Algebraic Approach to Find Some Topological Indices of Derived Graphs of the Benzene Ring

2021 ◽  
Vol 12 (4) ◽  
pp. 5431-5443
Keyword(s):  
Benzene Ring ◽  
Line Graph ◽  
Algebraic Approach ◽  
Chemical Compounds ◽  
Vital Role ◽  
Topological Indices ◽  
Zagreb Index ◽  
Subdivision Graph ◽  
Surface Network ◽  
P Type

Topological indices play a vital role in understanding the chemical and structural properties of the chemical compounds and nanostructures. By finding the M-polynomial of a graph representing a chemical compound, one can obtain the closed forms of some of the commonly known degree-based topological indices of the compound, such as the Zagreb index, general Randic ́ Index and harmonic index. In this article, we obtain the expression for the M-polynomial of the derived graphs of the Benzene ring embedded in the P-type surface network in 2D, namely the line graph, the subdivision graph, and the line graph of its subdivision. Furthermore, some of the degree-based topological indices are obtained for these graphs using their M-polynomials.

scholarly journals Computation of Vertex-Based Topological Descriptors of Organometallic Monolayers of TM 3 C 12 S 12

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Dalal Alrowaili ◽  
Faraha Ashraf ◽  
Rifaqat Ali ◽  
Arsalan Shoukat ◽  
Aqila Shaheen ◽  
...  
Keyword(s):  
Quantitative Structure Activity Relationship ◽  
Topological Descriptors ◽  
Quantitative Structure ◽  
Structure Property ◽  
Biological Structure ◽  
Qsar Modeling ◽  
Chemical Structures ◽  
Structure Activity ◽  
Structure Property Relationship ◽  
Mathematical Relationships

Topological descriptors are mathematical values related to chemical structures which are associated with different physicochemical properties. The use of topological descriptors has a great contribution in the field of quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) modeling. These are mathematical relationships between different molecular properties or biological activity and some other physicochemical or structural properties. In this article, we calculate few vertex degree-based topological indices/descriptors of the organometallic monolayer structure. At present, the numerical programming of the biological structure with topological descriptors is increasing in consequence in invigorating science, bioinformatics, and pharmaceutics.

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