A Note on Distance-Based Entropy of Dendrimers

Ghorbani, Modjtaba; Dehmer, Matthias; Zangi, Samaneh; Mowshowitz, Abbe; Emmert‐Streib, Frank

doi:10.3390/axioms8030098

Cited by 5 publications

(2 citation statements)

References 18 publications

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“…Problems in web mining, computational chemistry, engineering, and biology are examples of contributions that deal with a network (molecular) structural properties, such as statistical analysis of natural and synthetic chemical structures [19] and entropy and complexity of different graphs [20,21]. In 2019, Ghorbani et al [22] introduced a new entropy measure of a graph which involves the degree of the vertices and eccentricity known as eccentricity entropy. Before recalling this entropy measure, we recall relevant basic notions for a graph.…”

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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“…al. [19] formulated new distance (eccentricity), and eccentricity degree based entropy for molecular graphs namely, ecc‐entropy and ecc‐deg entropy. These entropies have vital significance due to their stronger prediction ability and highly correlated with ecc‐entropy alongside acentric factor of isomers (octane) which indicate one can study physical properties by calculating ecc‐deg entropy of different chemical structures [20–22].…”

Section: Introductionmentioning

confidence: 99%

On distance dependent entropy measures of poly propylene imine and zinc porphyrin dendrimers

Wei,

Fahad,

Raza

et al. 2024

Int J of Quantum Chemistry

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A key paradigm in contemporary research is the use of graphs to represent physical systems, molecular structures, or particularly metal frameworks. Graphs are increasingly widely used in a variety of fields, including the study of quantum and molecular systems, macromolecules and their interactions, socioeconomic and ecological systems, and technical and infra‐structural systems. Understanding how these systems function, are robust, and are stable begins with structural characterization. The use of entropies and entropy‐like measurements of graphs/structures of molecules/networks is crucial from both a mathematical and physical standpoint. Several entropy measures of graphs have been defined and studied extensively during the last few decades. The current paper is devoted to investigation of distance dependent entropy measures of Poly Propylene Imine (PPI) dendrimers and Zinc Porphyrin dendrimers. The analytical formulae of distance dependent entropy measures have been developed and their patterns have been presented through graphical tools.

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Informatics of chemical reactions: information entropy as the descriptor of changes in molecular complexity

Sabirov,

Tukhbatullina,

Zimina

et al. 2024

Russ Chem Bull

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A Note on Distance-Based Entropy of Dendrimers

Cited by 5 publications

References 18 publications

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

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

On distance dependent entropy measures of poly propylene imine and zinc porphyrin dendrimers

Informatics of chemical reactions: information entropy as the descriptor of changes in molecular complexity

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