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.

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.

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 measure of irregularities of nanosheets

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 419-431
Author(s):  
Zahid Iqbal ◽  
Muhammad Ishaq ◽  
Adnan Aslam ◽  
Muhammad Aamir ◽  
Wei Gao
Keyword(s):  
Statistical Approach ◽  
Chemical Properties ◽  
Polymeric Materials ◽  
Topological Descriptors ◽  
Quantitative Structure ◽  
Structure Property ◽  
Quantitative Characterization ◽  
Physical And Chemical ◽  
And Chemical Properties

AbstractNanosheets are two-dimensional polymeric materials, which are among the most active areas of investigation of chemistry and physics. Many diverse physicochemical properties of compounds are closely related to their underlying molecular topological descriptors. Thus, topological indices are fascinating beginning points to any statistical approach for attaining quantitative structure–activity (QSAR) and quantitative structure–property (QSPR) relationship studies. Irregularity measures are generally used for quantitative characterization of the topological structure of non-regular graphs. In various applications and problems in material engineering and chemistry, it is valuable to be well-informed of the irregularity of a molecular structure. Furthermore, the estimation of the irregularity of graphs is helpful for not only QSAR/QSPR studies but also different physical and chemical properties, including boiling and melting points, enthalpy of vaporization, entropy, toxicity, and resistance. In this article, we compute the irregularity measures of graphene nanosheet, H-naphtalenic nanosheet, {\text{SiO}}_{2} nanosheet, and the nanosheet covered by {C}_{3} and {C}_{6}.

scholarly journals Microscopy and Microanalysis of Nano-Scale Materials

2006 ◽  
Vol 14 (5) ◽  
pp. 6-15 ◽  
Author(s):  
J. R. Michael ◽  
L. N. Brewer ◽  
D. C. Miller ◽  
K. R. Zavadil ◽  
S. V. Prasad ◽  
...  
Keyword(s):  
Chemical Properties ◽  
Structure Property ◽  
Length Scales ◽  
Full Characterization ◽  
Microelectronic Devices ◽  
Structure Property Relationship ◽  
Scientists And Engineers ◽  
Physical And Chemical ◽  
And Chemical Properties

Material scientists and engineers continue to developmaterials and structures that are ever smaller. Some of this engineering is to simply domore with less while the science of nanomaterials allows new materials to be produced with a novel range of physical and chemical properties due to the small length scales of the microstructural features of thematerials. Currently, nanoscalematerials have been produced with a diverse set of useful properties and can be found in common substances like sunscreen or technologically advanced microelectronic devices. A complete understanding of materials is based on knowledge of the processing used to produce an interesting material coupled with a full characterization of the structure that results. It is this structure/property relationship that is the basis of understanding any newmaterial developed at all length scales.

scholarly journals Some Topological Measures for Nicotine

2020 ◽  
pp. 287-296
Author(s):  
Abaid ur Rehman Virk
Keyword(s):  
Topological Index ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Physical And Chemical Properties ◽  
Quantitative Structure ◽  
Structure Property ◽  
Structure Property Relationship ◽  
Topological Measures ◽  
Physical And Chemical ◽  
And Chemical Properties

A topological index is a quantity expressed as a number that help us to catch symmetry of chemical compounds. With the help of quantitative structure property relationship (QSPR), we can guess physical and chemical properties of several chemical compounds. Here, we will compute Shingali & Kanabour, Gourava and hype Gourava indices for the chemical compound Nicotine.

scholarly journals First reformulated Zagreb indices of some classes of graphs

2018 ◽  
Vol 9 (2) ◽  
pp. 134-144 ◽  
Author(s):  
V. Kaladevi ◽  
R. Murugesan ◽  
K. Pattabiraman
Keyword(s):  
Quantitative Structure Activity Relationship ◽  
Vital Role ◽  
Pictorial Representation ◽  
Quantitative Structure ◽  
Structure Property ◽  
Zagreb Index ◽  
Qsar Studies ◽  
Zagreb Indices ◽  
Subdivision Graph ◽  
Parallel Graph

A topological index of a graph is a parameter related to the graph; it does not depend on labeling or pictorial representation of the graph. Graph operations plays a vital role to analyze the structure and properties of a large graph which is derived from the smaller graphs. The Zagreb indices are the important topological indices found to have the applications in Quantitative Structure Property Relationship(QSPR) and Quantitative Structure Activity Relationship(QSAR) studies as well. There are various study of different versions of Zagreb indices. One of the most important Zagreb indices is the reformulated Zagreb index which is used in QSPR study. In this paper, we obtain the first reformulated Zagreb indices of some derived graphs such as double graph, extended double graph, thorn graph, subdivision vertex corona graph, subdivision graph and triangle parallel graph. In addition, we compute the first reformulated Zagreb indices of two important transformation graphs such as the generalized transformation graph and generalized Mycielskian 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 Irregularity Measures of Some Dendrimers Structures

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 271 ◽  
Author(s):  
Wei Gao ◽  
Muhammad Aamir ◽  
Zahid Iqbal ◽  
Muhammad Ishaq ◽  
Adnan Aslam
Keyword(s):  
Molecular Structure ◽  
Topological Structure ◽  
Enthalpy Of Vaporization ◽  
Regular Graphs ◽  
Quantitative Characterization ◽  
Molecular Graphs ◽  
Irregularity Index ◽  
Boiling Points ◽  
Vertex Degrees

A graph is said to be a regular graph if all its vertices have the same degree, otherwise, it is irregular. Irregularity indices are usually used for quantitative characterization of the topological structure of non-regular graphs. In numerous applications and problems in material engineering and chemistry, it is useful to be aware that how irregular a molecular structure is? Furthermore, evaluations of the irregularity of underline molecular graphs could be valuable for QSAR/QSPR studies, and for the expressive determines of chemical and physical properties, such as enthalpy of vaporization, toxicity, resistance, Entropy, melting and boiling points. In this paper, we think over the following four irregularity measures: the irregularity index by Albertson, σ irregularity index, the total irregularity index and the variance of vertex degrees. By way of graph structural estimation and derivations, we determine these irregularity measures of the molecular graphs of different classes of dendrimers.

scholarly journals On the irregularity of some molecular structures

2017 ◽  
Vol 95 (2) ◽  
pp. 174-183 ◽  
Author(s):  
Hosam Abdo ◽  
Darko Dimitrov ◽  
Wei Gao
Keyword(s):  
Structural Analysis ◽  
Chemical Properties ◽  
Molecular Structures ◽  
Molecular Graphs ◽  
Material Engineering ◽  
Irregularity Index ◽  
Boiling Points ◽  
Chemical Graphs ◽  
Vertex Degrees ◽  
And Chemical Properties

Measures of the irregularity of chemical graphs could be helpful for QSAR/QSPR studies and for the descriptive purposes of biological and chemical properties such as melting and boiling points, toxicity, and resistance. Here, we consider the following four established irregularity measures: the irregularity index by Albertson, the total irregularity, the variance of vertex degrees, and the Collatz–Sinogowitz index. Through the means of graph structural analysis and derivation, we study the above-mentioned irregularity measures of several chemical molecular graphs that frequently appear in chemical, medical, and material engineering, as well as the nanotubes: TUC4C8(S), TUC4C8(R), zigzag TUHC6, TUC4, Armchair TUVC6, then dendrimers Tk,d, and the circumcoronene series of benzenoid Hk. In addition, the irregularities of Mycielski’s constructions of cycle and path graphs are analyzed.

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