Multiplicative Zagreb Indices of Molecular Graphs
Mathematical modeling with the help of numerical coding of graphs has been used in the different fields of science, especially in chemistry for the studies of the molecular structures. It also plays a vital role in the study of the quantitative structure activities relationship (QSAR) and quantitati...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Chemistry |
| Online Access: | http://dx.doi.org/10.1155/2019/5294198 |
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| author | Xiujun Zhang H. M. Awais M. Javaid Muhammad Kamran Siddiqui |
| author_facet | Xiujun Zhang H. M. Awais M. Javaid Muhammad Kamran Siddiqui |
| author_sort | Xiujun Zhang |
| collection | DOAJ |
| description | Mathematical modeling with the help of numerical coding of graphs has been used in the different fields of science, especially in chemistry for the studies of the molecular structures. It also plays a vital role in the study of the quantitative structure activities relationship (QSAR) and quantitative structure properties relationship (QSPR) models. Todeshine et al. (2010) and Eliasi et al. (2012) defined two different versions of the 1st multiplicative Zagreb index as ∏Γ=∏p∈VΓdΓp2 and ∏1Γ=∏pq∈EΓdΓp+dΓq, respectively. In the same paper of Todeshine, they also defined the 2nd multiplicative Zagreb index as ∏2Γ=∏pq∈EΓdΓp×dΓq. Recently, Liu et al. [IEEE Access; 7(2019); 105479–-105488] defined the generalized subdivision-related operations of graphs and obtained the generalized F-sum graphs using these operations. They also computed the first and second Zagreb indices of the newly defined generalized F-sum graphs. In this paper, we extend this study and compute the upper bonds of the first multiplicative Zagreb and second multiplicative Zagreb indices of the generalized F-sum graphs. At the end, some particular results as applications of the obtained results for alkane are also included. |
| format | Article |
| id | doaj-art-e3c92f09dafb46e58cac9b244e351fcf |
| institution | Kabale University |
| issn | 2090-9063 2090-9071 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Chemistry |
| spelling | doaj-art-e3c92f09dafb46e58cac9b244e351fcf2025-08-20T03:26:33ZengWileyJournal of Chemistry2090-90632090-90712019-01-01201910.1155/2019/52941985294198Multiplicative Zagreb Indices of Molecular GraphsXiujun Zhang0H. M. Awais1M. Javaid2Muhammad Kamran Siddiqui3School of Information Science and Engineering, Chengdu University, Chengdu 610106, ChinaDepartment of Mathematics, School of Science, University of Management and Technology (UMT), Lahore 54770, PakistanDepartment of Mathematics, School of Science, University of Management and Technology (UMT), Lahore 54770, PakistanDepartment of Mathematics, COMSATS University Islamabad, Lahore Campus, Islamabad, PakistanMathematical modeling with the help of numerical coding of graphs has been used in the different fields of science, especially in chemistry for the studies of the molecular structures. It also plays a vital role in the study of the quantitative structure activities relationship (QSAR) and quantitative structure properties relationship (QSPR) models. Todeshine et al. (2010) and Eliasi et al. (2012) defined two different versions of the 1st multiplicative Zagreb index as ∏Γ=∏p∈VΓdΓp2 and ∏1Γ=∏pq∈EΓdΓp+dΓq, respectively. In the same paper of Todeshine, they also defined the 2nd multiplicative Zagreb index as ∏2Γ=∏pq∈EΓdΓp×dΓq. Recently, Liu et al. [IEEE Access; 7(2019); 105479–-105488] defined the generalized subdivision-related operations of graphs and obtained the generalized F-sum graphs using these operations. They also computed the first and second Zagreb indices of the newly defined generalized F-sum graphs. In this paper, we extend this study and compute the upper bonds of the first multiplicative Zagreb and second multiplicative Zagreb indices of the generalized F-sum graphs. At the end, some particular results as applications of the obtained results for alkane are also included.http://dx.doi.org/10.1155/2019/5294198 |
| spellingShingle | Xiujun Zhang H. M. Awais M. Javaid Muhammad Kamran Siddiqui Multiplicative Zagreb Indices of Molecular Graphs Journal of Chemistry |
| title | Multiplicative Zagreb Indices of Molecular Graphs |
| title_full | Multiplicative Zagreb Indices of Molecular Graphs |
| title_fullStr | Multiplicative Zagreb Indices of Molecular Graphs |
| title_full_unstemmed | Multiplicative Zagreb Indices of Molecular Graphs |
| title_short | Multiplicative Zagreb Indices of Molecular Graphs |
| title_sort | multiplicative zagreb indices of molecular graphs |
| url | http://dx.doi.org/10.1155/2019/5294198 |
| work_keys_str_mv | AT xiujunzhang multiplicativezagrebindicesofmoleculargraphs AT hmawais multiplicativezagrebindicesofmoleculargraphs AT mjavaid multiplicativezagrebindicesofmoleculargraphs AT muhammadkamransiddiqui multiplicativezagrebindicesofmoleculargraphs |