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.

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 On Ve-Degree-Based Irregularity Properties of the Crystallographic Structure of Molecules

2021 ◽  
Vol 2021 ◽  
pp. 1-22
Author(s):  
Akbar Jahanbani ◽  
Rana Khoeilar ◽  
Hajar Shooshtari
Keyword(s):  
Molecular Structure ◽  
Complex Network ◽  
Topological Structure ◽  
Organic Molecules ◽  
Crystallographic Structure ◽  
Quantitative Characterization ◽  
Material Engineering ◽  
Structure Of Molecules ◽  
Crystallographic Structures

Irregularity indices are usually used for quantitative characterization of the topological structure of nonregular graphs. In numerous applications and problems in material engineering and chemistry, it is useful to be aware that how irregular a molecular structure is? In this paper, we are interested in formulating closed forms of irregularity measures of some of the crystallographic structures of Cu 2 O p , q , r and crystallographic structure of titanium difluoride of T i F 2 p , q , r . These theoretical conclusions provide practical guiding significance for pharmaceutical engineering and complex network and quantify the degree of folding of long organic molecules.

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 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.

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 Graph of atomic orbitals and the molecular structure-descriptors based on it

2005 ◽  
Vol 70 (4) ◽  
pp. 669-674 ◽  
Author(s):  
Andrey Toropov ◽  
Ivan Gutman ◽  
Boris Furtula
Keyword(s):  
Molecular Structure ◽  
Molecular Graph ◽  
Atomic Orbitals ◽  
Molecular Graphs ◽  
Boiling Points ◽  
Better Than

The graph of atomic orbitals (GAO) is a novel type of molecular graph recently proposed by one of the authors. Various molecular structure-descriptors computed for GAO are compared with their analogs computed for ordinary molecular graphs. The quality of these structure-descriptors was tested for correlation with the normal boiling points of alkanes and cycloalkanes. In all the studied cases, the results based on GAO are similar to, and usually slightly better than, those obtained by means of ordinary molecular graps.

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