Irregularity Measures of Subdivision Vertex-Edge Join of Graphs

Zheng, Jialin; Akhter, Shehnaz; Iqbal, Zahid; Shafiq, Muhammad Kashif; Aslam, Adnan; Ishaq, Muhammad; Aamir, Muhammad

doi:10.1155/2021/6673221

Cited by 7 publications

(5 citation statements)

References 36 publications

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“…Since the structure of a molecule depends on the covalent bonds among its atoms, so the numerical graph invariants obtained from the information based on vertices and edges can disseminate structural information about the molecule. Several aspects of TIs and their applications, such as the Mostar index for nanostructures and graph operations [5,6], topological aspects of lattice, metal-organic superlattice and dendrimers [3,7,8], irregularity measures for different derived graphs [9,10], eccentric-connectivity polynomial and distancedependent entropies [11][12][13], have been studied extensively over the years.…”

Section: Introductionmentioning

confidence: 99%

On Entropy Measures and Eccentricity-Based Descriptors of Polyamidoamine (PAMAM) Dendrimers

Hui

Fahad

Qureshi

et al. 2022

Journal of Chemistry

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Topological indices (TIs) assign a numeric value to a graph or a molecular structure. Due to their ability to predict the physiochemical properties of a molecular graph, several TIs have been introduced and studied, mainly based on degree and distance. For a vertex v , the maximum distance of v from any other vertex in a graph G is called the eccentricity of v , which is denoted by σ v , in G . The eccentricity of vertices gained special attention among the distance-based or degree-distance based TIs. An important TI in the class of eccentricity-dependent TIs is an eccentricity-entropy index. Furthermore, other eccentricity-dependent TIs such as eccentric-connectivity index, total-eccentricity index, and the first Zagreb index have also been extensively studied. On the other hand, dendrimers came out as unique polymeric macromolecules because of extensively branched three-dimensional architectural characteristics. This structure design prepares for various unique properties of dendrimers, including monodispersity, multivalency, uniform size, globular shape, water solubility with hydrophobic internal cavities, and a high degree of branching. These properties make them attractive candidates for different applications. PAMAM (polyamidoamine) dendrimers are promising polymers that can be successfully used in various biomedical applications. The PAMAM dendrimers having different structures such as a primary amine as the end group or porphyrin core have been studied through graph-theoretic parameters. This paper studies these two types of PAMAM dendrimers through eccentricity-dependent parameters. In particular, we establish formulae of eccentricity entropy for two types of PAMAM dendrimers. Moreover, we also derive analytic formulae of some other significant TIs from the class of eccentricity-dependent TIs. Furthermore, we apply graphical tools to demonstrate the trends of the values in the obtained results.

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Section: Introductionmentioning

confidence: 99%

On Entropy Measures and Eccentricity-Based Descriptors of Polyamidoamine (PAMAM) Dendrimers

Hui

Fahad

Qureshi

et al. 2022

Journal of Chemistry

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“…e recent work and development of irregularity indices can be seen more elaborately in [25][26][27][28][29].…”

Section: Irregularity-based Indices For Qspr Analysismentioning

confidence: 99%

VDB Entropy Measures and Irregularity-Based Indices for the Rectangular Kekulene System

Zhao

Julietraja²,

Venugopal

et al. 2021

Journal of Mathematics

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Theoretical chemists are fascinated by polycyclic aromatic hydrocarbons (PAHs) because of their unique electromagnetic and other significant properties, such as superaromaticity. The study of PAHs has been steadily increasing because of their wide-ranging applications in several fields, like steel manufacturing, shale oil extraction, coal gasification, production of coke, tar distillation, and nanosciences. Topological indices (TIs) are numerical quantities that give a mathematical expression for the chemical structures. They are useful and cost-effective tools for predicting the properties of chemical compounds theoretically. Entropic network measures are a type of TIs with a broad array of applications, involving quantitative characterization of molecular structures and the investigation of some specific chemical properties of molecular graphs. Irregularity indices are numerical parameters that quantify the irregularity of a molecular graph and are used to predict some of the chemical properties, including boiling points, resistance, enthalpy of vaporization, entropy, melting points, and toxicity. This study aims to determine analytical expressions for the VDB entropy and irregularity-based indices in the rectangular Kekulene system.

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“…A topological index is a computational parameter derived from the graph structure mathematically [9][10][11][12][13]. To visualize the relationships between the data sets, graphs are crucial tools which make the concept better understandable.…”

Section: Introduction and Terminologiesmentioning

confidence: 99%

Computing SS Index of Certain Dendrimers

Zhao

Shanmukha

Usha

et al. 2021

Journal of Mathematics

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The numerical descriptor gathers the data from the molecular graphs and helps to know the characteristics of the chemical structure known as topological index. The QSAR/QSPR/QSTR studies are benefited with the significant role played by topological indices in the drug design. Topological indices provide the information about the physical/chemical/biological properties of chemical compounds. The Zagreb indices are widely studied because of their extensive usage in chemical graph theory. Inspired by the earlier work on inverse sum indeg index (ISI index), novel topological index known as SS index is introduced and computed for four dendrimer structures. Also, the strong correlation coefficient between SS index and 5 physico-chemical characteristics such as boiling point (bp), molar volume (mv), molar refraction (mr), heats of vaporization (hv), and critical pressure (cp) of 67 alkane isomers have been determined. It is found that newly introduced index has shown good correlation in comparison with three most popular existing indices (ISI index and first and second Zagreb indices). In the last part, the mathematical properties of SS index are discussed.

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Irregularity Measures of Subdivision Vertex-Edge Join of Graphs

Cited by 7 publications

References 36 publications

On Entropy Measures and Eccentricity-Based Descriptors of Polyamidoamine (PAMAM) Dendrimers

On Entropy Measures and Eccentricity-Based Descriptors of Polyamidoamine (PAMAM) Dendrimers

VDB Entropy Measures and Irregularity-Based Indices for the Rectangular Kekulene System

Computing SS Index of Certain Dendrimers

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