On Entropy Measures and Eccentricity-Based Descriptors of Polyamidoamine (PAMAM) Dendrimers
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...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Chemistry |
| Online Access: | http://dx.doi.org/10.1155/2022/1214137 |
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| author | Zhi-Hao Hui Asfand Fahad Muhammad Imran Qureshi Rida Irfan Aneesa Shireen Zahid Iqbal Rahma Alyusufi |
| author_facet | Zhi-Hao Hui Asfand Fahad Muhammad Imran Qureshi Rida Irfan Aneesa Shireen Zahid Iqbal Rahma Alyusufi |
| author_sort | Zhi-Hao Hui |
| collection | DOAJ |
| description | 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 σv, 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. |
| format | Article |
| id | doaj-art-cdafaa12a7514da186214ddf72a5978d |
| institution | Kabale University |
| issn | 2090-9071 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Chemistry |
| spelling | doaj-art-cdafaa12a7514da186214ddf72a5978d2025-02-03T06:11:50ZengWileyJournal of Chemistry2090-90712022-01-01202210.1155/2022/1214137On Entropy Measures and Eccentricity-Based Descriptors of Polyamidoamine (PAMAM) DendrimersZhi-Hao Hui0Asfand Fahad1Muhammad Imran Qureshi2Rida Irfan3Aneesa Shireen4Zahid Iqbal5Rahma Alyusufi6School of Mathematics and StatisticsCentre for Advanced Studies in Pure and Applied MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of Mathematics and StatisticsDepartment of MathematicsTopological 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 σv, 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.http://dx.doi.org/10.1155/2022/1214137 |
| spellingShingle | Zhi-Hao Hui Asfand Fahad Muhammad Imran Qureshi Rida Irfan Aneesa Shireen Zahid Iqbal Rahma Alyusufi On Entropy Measures and Eccentricity-Based Descriptors of Polyamidoamine (PAMAM) Dendrimers Journal of Chemistry |
| title | On Entropy Measures and Eccentricity-Based Descriptors of Polyamidoamine (PAMAM) Dendrimers |
| title_full | On Entropy Measures and Eccentricity-Based Descriptors of Polyamidoamine (PAMAM) Dendrimers |
| title_fullStr | On Entropy Measures and Eccentricity-Based Descriptors of Polyamidoamine (PAMAM) Dendrimers |
| title_full_unstemmed | On Entropy Measures and Eccentricity-Based Descriptors of Polyamidoamine (PAMAM) Dendrimers |
| title_short | On Entropy Measures and Eccentricity-Based Descriptors of Polyamidoamine (PAMAM) Dendrimers |
| title_sort | on entropy measures and eccentricity based descriptors of polyamidoamine pamam dendrimers |
| url | http://dx.doi.org/10.1155/2022/1214137 |
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