scholarly journals Irregularity Measures of Subdivision Vertex-Edge Join of Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Jialin Zheng ◽  
Shehnaz Akhter ◽  
Zahid Iqbal ◽  
Muhammad Kashif Shafiq ◽  
Adnan Aslam ◽  
...  
Keyword(s):  
Quantitative Structure Activity Relationship ◽  
Quantitative Structure ◽  
Structure Property ◽  
Irregularity Index ◽  
Graphs And Networks ◽  
Challenging Tasks ◽  
Topological Measures ◽  
Join Of Graphs ◽  
Vertex Degrees

The study of graphs and networks accomplished by topological measures plays an applicable task to obtain their hidden topologies. This procedure has been greatly used in cheminformatics, bioinformatics, and biomedicine, where estimations based on graph invariants have been made available for effectively communicating with the different challenging tasks. Irregularity measures are mostly used for the characterization of the nonregular graphs. In several applications and problems in various areas of research like material engineering and chemistry, it is helpful to be well-informed about the irregularity of the underline structure. Furthermore, the irregularity indices of graphs are not only suitable for quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR) studies but also for a number of chemical and physical properties, including toxicity, enthalpy of vaporization, resistance, boiling and melting points, and entropy. In this article, we compute the irregularity measures including the variance of vertex degrees, the total irregularity index, the σ irregularity index, and the Gini index of a new graph operation.

scholarly journals Comparison of Irregularity Indices of Several Dendrimers Structures

Processes ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 662 ◽  
Author(s):  
Dongming Zhao ◽  
Zahid Iqbal ◽  
Rida Irfan ◽  
Muhammad Anwar Chaudhry ◽  
Muhammad Ishaq ◽  
...  
Keyword(s):  
Chemical Properties ◽  
Quantitative Structure Activity Relationship ◽  
Quantitative Structure ◽  
Structure Property ◽  
Qsar Studies ◽  
Irregularity Index ◽  
Boiling Points ◽  
Vertex Degrees ◽  
Physical And Chemical

Irregularity indices are usually used for quantitative characterization of the topological structures of non-regular graphs. In numerous problems and applications, especially in the fields of chemistry and material engineering, it is useful to be aware of the irregularity of a molecular structure. Furthermore, the evaluation of the irregularity of graphs is valuable not only for quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies but also for various physical and chemical properties, including entropy, enthalpy of vaporization, melting and boiling points, resistance, and toxicity. In this paper, we will restrict our attention to the computation and comparison of the irregularity measures of different classes of dendrimers. The four irregularity indices which we are going to investigate are σ irregularity index, the irregularity index by Albertson, the variance of vertex degrees, and the total irregularity index.

Characteristic study of irregularity measures of some nanotubes

2019 ◽  
Vol 97 (10) ◽  
pp. 1125-1132 ◽  
Author(s):  
Zahid Iqbal ◽  
Adnan Aslam ◽  
Muhammad Ishaq ◽  
Muhammad Aamir
Keyword(s):  
Quantitative Structure ◽  
Structure Property ◽  
Know How ◽  
Molecular Graphs ◽  
Irregularity Index ◽  
Structure Property Relationships ◽  
Boiling Points ◽  
Quantitative Structure Property Relationships ◽  
Quantitative Structure Activity Relationships ◽  
Vertex Degrees

In many applications and problems in material engineering and chemistry, it is valuable to know how irregular a given molecular structure is. Furthermore, measures of the irregularity of underlying molecular graphs could be helpful for quantitative structure property relationships and quantitative structure-activity relationships studies, and for determining and expressing chemical and physical properties, such as toxicity, resistance, and melting and boiling points. Here we explore the following three irregularity measures: the irregularity index by Albertson, the total irregularity, and the variance of vertex degrees. Using graph structural analysis and derivation, we compute the above-mentioned irregularity measures of several molecular graphs of nanotubes.

scholarly journals The Second Hyper-Zagreb Index of Complement Graphs and Its Applications of Some Nano Structures

2021 ◽  
pp. 54-75
Author(s):  
Mohammed Alsharafi ◽  
Yusuf Zeren ◽  
Abdu Alameri
Keyword(s):  
Graph Theory ◽  
Cartesian Product ◽  
Quantitative Structure Activity Relationship ◽  
Quantitative Structure ◽  
Structure Property ◽  
Zagreb Index ◽  
Chemical Graph ◽  
Strong Product ◽  
Chemical Graph Theory ◽  
Mathematical Operations

In chemical graph theory, a topological descriptor is a numerical quantity that is based on the chemical structure of underlying chemical compound. Topological indices play an important role in chemical graph theory especially in the quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR). In this paper, we present explicit formulae for some basic mathematical operations for the second hyper-Zagreb index of complement graph containing the join G1 + G2, tensor product G1 \(\otimes\) G2, Cartesian product G1 x G2, composition G1 \(\circ\) G2, strong product G1 * G2, disjunction G1 V G2 and symmetric difference G1 \(\oplus\) G2. Moreover, we studied the second hyper-Zagreb index for some certain important physicochemical structures such as molecular complement graphs of V-Phenylenic Nanotube V PHX[q, p], V-Phenylenic Nanotorus V PHY [m, n] and Titania Nanotubes TiO2.

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.

On Certain Topological Indices of Three-Layered Single-Walled Titania Nanosheets

2020 ◽  
Vol 23 ◽  
Author(s):  
Micheal Arockiaraj ◽  
Jia-Bao Liu ◽  
M. Arulperumjothi ◽  
S. Prabhu
Keyword(s):  
Materials Science ◽  
Molecular Graph ◽  
Quantitative Structure Activity Relationship ◽  
Topological Indices ◽  
Quantitative Structure ◽  
Structure Property ◽  
Mathematical Properties ◽  
Chemical Graph Theory ◽  
Research Article ◽  
Cut Method

Aim and Objective: Nanostructures are objects whose sizes are between microscopic and molecular. The most significant of these new elements are carbon nanotubes. These elements have extraordinary microelectronic properties and many other exclusive physiognomies. Recently, researchers have given the attention to the mathematical properties of these materials. The aim and objective of this research article is to investigate the most important molecular descriptors namely Wiener, edge-Wiener, vertex-edge-Wiener, vertex-Szeged, edge-Szeged, edge-vertex-Szeged, total-Szeged, PI, Schultz, Gutman, Mostar, edge-Mostar, and total-Mostar indices of three-layered single-walled titania nanosheets. By computing these topological indices, materials science researchers can have a better understanding of structural and physical properties of titania nanosheets, and thereby more easily synthesizing new variants of titania nanosheets with more amenable physicochemical properties. Methods: The cut method turned out to be extremely handy when dealing with distance-based graph invariants which are in turn among the central concepts of chemical graph theory. In this method, we use the Djokovic ́-Winkler relation to find the suitable edge cuts to leave the graph into exactly two components. Based on the graph theoretical measures of the components, we obtain the desired topological indices by mathematical computations. Results: In this paper, distance-based indices for three-layered single-walled titania nanosheets were investigated and given the exact expressions for various dimensions of three-layered single-walled titania nanosheets. These indices may be useful in synthesizing new variants of titania nanosheets and the computed topological indices play an important role in studies of Quantitative structure-activity relationship (QSAR) and Quantitative structure-property relationship (QSPR). Conclusion: In this paper, we have obtained the closed expressions of several distance-based topological indices of three-layered single-walled titania nanosheet TNS_3 [m,n] molecular graph for the cases m≥ n and m < n. The graphical validations for the computed indices are done and we observe that the Wiener types, Schultz and Gutman indices perform in a similar way whereas PI and Mostar type indices perform in the same way.

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 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.

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