Degree-based topological indices of geranyl and farnesyl penicillin G bioconjugate structure

Rauf, Abdul; Maqbool, Saba; Aslam, Adnan

doi:10.1140/epjp/s13360-022-02513-0

Cited by 9 publications

(6 citation statements)

References 34 publications

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“…The Ve-degree of the vertex s, denoted by J s , is equal to the number of edges connecting any vertex in the vertex s's closed neighborhood. For basic terminologies related to graph theory, see [36], and the below-defined entropy indices can be seen in [19,29,30,34]. The definition of the entropy function is as follows:…”

Section: Ve-degree Based Entropy Of Graphmentioning

confidence: 99%

“…The Ve‐degree of the vertex

s

, denoted by

𝕁_{s}

, is equal to the number of edges connecting any vertex in the vertex

s

's closed neighborhood. For basic terminologies related to graph theory, see [36], and the below‐defined entropy indices can be seen in [19,29,30,34]. The definition of the entropy function is as follows:

ℰ_{ℍ} false(P false) = prefix- \sum_{i = 1}^{p} \frac{ℍ false(s_{i} false)}{\sum_{j = 1}^{p} ℍ false(s_{i} false)} l o g ([], \frac{ℍ false(s_{i} false)}{\sum_{j = 1}^{p} ℍ false(s_{i} false)}) .

Now, if

s_{i} \in V

and

ℍ false(s_{i} false)

is an information function that represent the vertex degree of

s_{i}

, denoted by

ℍ false(s_{i} false) = 𝕁_{s_{i}}

, then Equation () becomes

ℰ_{ℍ} false(P false) = prefix- \sum_{i = 1}^{p} \frac{𝕁_{s_{i}}}{\sum_{j = 1}^{p} 𝕁_{s_{i}}} l o g ([], \frac{𝕁_{s_{i}}}{\sum_{j = 1}^{p}})

…”

Section: Preliminariesmentioning

confidence: 99%

“…The redefined Zagreb index of a graph was defined by Ranjini et al [16]. The reader may see [17][18][19][20][21][22] for more information on topological indices and their applications.…”

mentioning

confidence: 99%

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Quality testing analysis of Ve‐degree based entropies by using benzene derivatives

Hui

Rauf

Aslam

et al. 2023

Int J of Quantum Chemistry

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A topological index, also known as a connectedness index, is a numerical characteristic of chemical structure that is computed by using its molecular graph in theoretical chemistry. In quantitative structure-activity relationships (QSARs), which relate a molecule's chemical structure to its physical and chemical properties, topological indices are employed. The graph entropies with topological indices were inspired by Shannon's entropy concept and became the information-theoretic quantities for measuring the structural information of chemical graphs. The theory of graphs is useful in determining the relationship between specific properties of chemical structures using different graph entropy measures. Through these entropies, many physical and chemical characteristics, such as melting point, energy generation, Henry's Law, and molar mass of chemical compounds, can be calculated. For this, the quantitative structure-property relationship (QSPR) models are designed using ve-degree-based entropies to examine some physical properties of benzene derivatives. For the computation of entropies, a Maple-based program is developed. The QSPR study is performed using SPSS and linear regression techniques. In this work, we have observed that the redefined third Zagreb entropy, the Balaban entropy, and the Randic entropy are the best predictors.The physiochemical characteristics, namely Henry's Law and critical pressure, can be predicted by Randic entropy and Balaban entropy, respectively. The redefined third Zagreb entropy can predict four other properties: enthalpy, molar mass, π-electronic energy, and molecular weight.benzene derivatives, entropy measures, physio-chemical characteristics, QSPR, Ve-degree | INTRODUCTIONChemical graph theory (CGT) is a field of mathematical chemistry that employs graph theory methods to develop chemical phenomena quantitatively.CGT also connects to nontrivial graph theory applications for tackling molecular difficulties. In the field of chemical sciences, this hypothesis has a lot of applications [1,2]. To predict the physio-chemical properties of chemical compounds, quantitative structure-property relationship (QSPR)/quantitative structure-activity relationship (QSAR) are used [3].A topological index is a numerical value that is derived theoretically by utilizing the molecular graph. It is linked to chemical composition, revealing the link between chemical structure and a variety of physical, chemical, and biological properties. Among the different topological indices, the most studied are those depending on the degree of end vertices of the underlying graph. The first degree-based topological index was proposed by Randic [4] in 1975. Later, many topological indices were introduced by different researchers with applications to QSPR/QSAR

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Section: Ve-degree Based Entropy Of Graphmentioning

confidence: 99%

“…The Ve‐degree of the vertex

s

, denoted by

𝕁_{s}

, is equal to the number of edges connecting any vertex in the vertex

s

ℰ_{ℍ} false(P false) = prefix- \sum_{i = 1}^{p} \frac{ℍ false(s_{i} false)}{\sum_{j = 1}^{p} ℍ false(s_{i} false)} l o g ([], \frac{ℍ false(s_{i} false)}{\sum_{j = 1}^{p} ℍ false(s_{i} false)}) .

Now, if

s_{i} \in V

and

ℍ false(s_{i} false)

is an information function that represent the vertex degree of

s_{i}

, denoted by

ℍ false(s_{i} false) = 𝕁_{s_{i}}

, then Equation () becomes

ℰ_{ℍ} false(P false) = prefix- \sum_{i = 1}^{p} \frac{𝕁_{s_{i}}}{\sum_{j = 1}^{p} 𝕁_{s_{i}}} l o g ([], \frac{𝕁_{s_{i}}}{\sum_{j = 1}^{p}})

…”

Section: Preliminariesmentioning

confidence: 99%

See 1 more Smart Citation

Quality testing analysis of Ve‐degree based entropies by using benzene derivatives

Hui

Rauf

Aslam

et al. 2023

Int J of Quantum Chemistry

Self Cite

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show abstract

“…See [34][35][36][37][38][39][40][41][42][43] for further information on these defined topological indices.…”

Section: Introductionmentioning

confidence: 99%

Study of Ge‐Sb‐Te Superlattice Structure Based on Topological Descriptors

Zhang

Rauf

Aslam

et al. 2022

Journal of Mathematics

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Ge-Sb-Te superlattice is a new electronic material that is capable of storing nonvolatile phase-change memories with very low energy consumption. Topological descriptors are numerical values given to molecular structures that may be used to predict specific physical/chemical characteristics. In this work, we have investigated topological descriptors of the Ge-Sb-Te superlattice structure based on ev and ve-degree. We have calculated the Zagreb, geometric-arithmetic, Randic, and atom-bond connectivity indices of the Ge-Sb-Te superlattice structure using the ev- and ve-degrees. This kind of research may be beneficial for understanding the structure’s chemical and biological activity.

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“…The atom bond connectivity index admits a strong link with heat of formation of branched alkanes and the strain energy of cycloalkanes [14,15]. Recently, the geometric arithmetic and atom bond connectivity indices of Guar gum and its derivatives [16], linear graphs of molecular cactus chain networks and their subdivisions [17], geranyl and farnesyl penicillin G bioconjugate with and without a sensitive bond [18], drugs used for the treatment of breast cancer [19] and polycyclic aromatic hydrocarbons [20] are calculated to relate with the QSPR.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Productive Topological Index Correlated to Fullerenes’ Physical Properties

et al. 2022

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Fullerene is a cage-like carbon allotrope admitting a vast range of applications. Some of the important fullerenes are C54,C58,C60,C70,C74,C76,C78,C80C82,C84,C86,C90. The physical properties of fullerenes can be exhibited using the degree-based topological indices. The sum based geometric arithmetic index is significant in this manner. The sum based atomic bond connectivity, Randic, first and second Zagreb indices are well known topological indices. We have determined the regression relation between each of these indices and the sum based geometric arithmetic index. Moreover, the correlation coefficient is also calculated. Correlation is a symmetric relation, as it provides association between two variables. On the basis of regression analysis and correlation coefficient, it was found that each of this index is strongly related to the sum based geometric arithmetic index. Moreover, we have computed the regression relations concerning the physical properties depending on the sum based geometric arithmetic index. The physical properties include binding energies, Ramsauer-Townsend minima, shape resonances and heat of formation of fullerene molecules. It was concluded that the sum based GA index is the best in presenting the heat of the formation of molecules.

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Degree-based topological indices of geranyl and farnesyl penicillin G bioconjugate structure

Cited by 9 publications

References 34 publications

Quality testing analysis of Ve‐degree based entropies by using benzene derivatives

Quality testing analysis of Ve‐degree based entropies by using benzene derivatives

Study of Ge‐Sb‐Te Superlattice Structure Based on Topological Descriptors

Analysis of a Productive Topological Index Correlated to Fullerenes’ Physical Properties

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