scholarly journals Second Zagreb and Sigma Indices of Semi and Total Transformations of Graphs

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Zhen Yang ◽  
Micheal Arockiaraj ◽  
Savari Prabhu ◽  
M. Arulperumjothi ◽  
Jia-Bao Liu
Keyword(s):  
Physicochemical Properties ◽  
Molecular Graph ◽  
Vital Role ◽  
Topological Indices ◽  
The Novel ◽  
Structure Property ◽  
Bond Type ◽  
Property Relations

The study of structure-property relations including the transformations of molecules is of utmost importance in correlations with corresponding physicochemical properties. The graph topological indices have been used effectively for such study and, in particular, bond-based indices play a vital role. The bond-additive topological indices of a molecular graph are defined as a sum of edge measures over all edges in which edge measures can be computed based on degrees, closeness, peripherality, and irregularity. In this study, we provide the mathematical characterization of the transformation of a structure that can be accomplished by the novel edge adjacency and incidence relations. We derive the exact expressions of bond type indices such as second Zagreb, sigma indices, and their coindices of total transformation and two types of semitransformations of the molecules which in turn can be used to characterize the topochemical and topostructural properties.

scholarly journals Multiblock Copolymers of Norbornene and Cyclododecene: Chain Structure and Properties

Polymers ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 1756
Author(s):  
Yulia I. Denisova ◽  
Georgiy A. Shandryuk ◽  
Marianna P. Arinina ◽  
Ivan S. Levin ◽  
Vsevolod A. Zhigarev ◽  
...  
Keyword(s):  
First Generation ◽  
Average Length ◽  
Chain Structure ◽  
Random Copolymers ◽  
Multiblock Copolymers ◽  
Structure Property ◽  
Reaction Conditions ◽  
Property Relations ◽  
Cross Metathesis

We investigate the structure–property relations of the multiblock copolymers of norbornene with cyclododecene synthesized via the macromolecular cross-metathesis reaction between amorphous polynorbornene and semicrystalline polydodecenamer in the presence of the first-generation Grubbs catalyst. By adjusting the reaction time, catalyst amount, and composition of the initial system, we obtain a set of statistical multiblock copolymers that differ in the composition and average length of norbornene and dodecenylene unit sequences. Structural, thermal, and mechanical characterization of the copolymers with NMR, XRD, DSC (including thermal fractionation by successive self-nucleation and annealing), and rotational rheology allows us to relate the reaction conditions to the average length of crystallizable unit sequences, thicknesses of corresponding lamellas, and temperatures of their melting. We demonstrate that isolated dodecenylene units can be incorporated into crystalline lamellas so that even nearly random copolymers should retain crystallinity. Weak high-temperature endotherms observed in the multiblock copolymers of norbornene with cyclododecene and other cycloolefins could indicate that the corresponding systems are microphase-separated in the melt state.

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 Editorial: Topological investigations of chemical networks

2021 ◽  
Vol 44 (1) ◽  
pp. 267-269
Author(s):  
Muhammad Javaid ◽  
Muhammad Imran
Keyword(s):  
Information Science ◽  
Biological Activities ◽  
Chemical Properties ◽  
Vital Role ◽  
Topological Indices ◽  
Molecular Structures ◽  
Quantitative Structure ◽  
Structure Property ◽  
Chemical Structures ◽  
Interdisciplinary Field

Abstract The topic of computing the topological indices (TIs) being a graph-theoretic modeling of the networks or discrete structures has become an important area of research nowadays because of its immense applications in various branches of the applied sciences. TIs have played a vital role in mathematical chemistry since the pioneering work of famous chemist Harry Wiener in 1947. However, in recent years, their capability and popularity has increased significantly because of the findings of the different physical and chemical investigations in the various chemical networks and the structures arising from the drug designs. In additions, TIs are also frequently used to study the quantitative structure property relationships (QSPRs) and quantitative structure activity relationships (QSARs) models which correlate the chemical structures with their physio-chemical properties and biological activities in a dataset of chemicals. These models are very important and useful for the research community working in the wider area of cheminformatics which is an interdisciplinary field combining mathematics, chemistry, and information science. The aim of this editorial is to arrange new methods, techniques, models, and algorithms to study the various theoretical and computational aspects of the different types of these topological indices for the various molecular structures.

scholarly journals HDR Degree Bassed Indices and Mhr-Polynomial for the Treatment of COVID-19

2021 ◽  
Vol 12 (6) ◽  
pp. 7214-7225
Keyword(s):  
Regression Analysis ◽  
Physicochemical Properties ◽  
Topological Index ◽  
Research Work ◽  
Topological Indices ◽  
Structure Property ◽  
Zagreb Index ◽  
Mathematical Properties ◽  
Octane Isomers

In this research work, We introduce topological indices, namely as an HDR version of Modified Zagreb topological index (HDRM*), HDR version of Modified forgotten topological index (HDRF*), and HDR version of hyper Zagreb index (HDRHM*). Then the relatively study depends on the structure-property regression analysis to test and compute the chemical applicability of these indices to predict the physicochemical properties of octane isomers. Also, we show these HDR indices have well degeneracy properties compared to other degree-based topological indices. Also, We defined and computed the Mhr-polynomial of the newly indices and applied it on COVID-19 treatments. Also, we discussed some mathematical properties of HDR indices.

scholarly journals On Ve-Degree and Ev-Degree Topological Properties of Hyaluronic Acid‐Anticancer Drug Conjugates with QSPR

2021 ◽  
Vol 2021 ◽  
pp. 1-23
Author(s):  
Syed Ajaz K. Kirmani ◽  
Parvez Ali ◽  
Faizul Azam ◽  
Parvez Ahmad Alvi
Keyword(s):  
Molecular Structure ◽  
Hyaluronic Acid ◽  
Biological Activities ◽  
Molecular Graph ◽  
Topological Indices ◽  
Structure Property ◽  
Zagreb Index ◽  
Anticancer Properties ◽  
Drug Conjugates ◽  
Molecular Structure Analysis

The design of the quantitative structure-property/activity relationships for drug-related compounds using theoretical methods relies on appropriate molecular structure representations. The molecular structure of a compound comprises all the information required to determine its chemical, biological, and physical properties. These properties can be assessed by employing a graph theoretical descriptor tool widely known as topological indices. Generalization of descriptors may reduce not only the number of molecular graph-based descriptors but also improve existing results and provide a better correlation to several molecular properties. Recently introduced ve-degree and ev-degree topological indices have been successfully employed for development of models for the prediction of various biological activities/properties. In this article, we propose the general ve-inverse sum indeg index ISI α , β ve G and general ve-Zagreb index M α ve G of graph G and compute ISI α , β ve G , M α ve G , and M α ev G (general ev-degree index) of hyaluronic acid-curcumin/paclitaxel conjugates, renowned for its potential anti-inflammatory, antioxidant, and anticancer properties, by using molecular structure analysis and edge partitioning technique. Several ve-degree- and ev-degree-based topological indices are obtained as a special case of ISI α , β ve G , M α ve G , and M α ev G . Furthermore, QSPR analysis of ISI α , β ve G , M α ve G , and M α ev G for particular values of α and β is performed, which reveals their predicting power. These results allow researchers to better understand the physicochemical properties and pharmacological characteristics of these conjugates.

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