Forgotten Coindex for the Derived Sum Graphs under Cartesian Product
A topological index (TI) is a molecular descriptor that is applied on a chemical structure to compute the associated numerical value which measures volume, density, boiling point, melting point, surface tension, or solubility of this structure. It is an efficient mathematical method in avoiding labo...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Journal of Chemistry |
| Online Access: | http://dx.doi.org/10.1155/2021/3235068 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832557051871494144 |
|---|---|
| author | Muhammad Ibraheem Meshari M. Aljohani Muhammad Javaid Abdulaziz Mohammed Alanazi |
| author_facet | Muhammad Ibraheem Meshari M. Aljohani Muhammad Javaid Abdulaziz Mohammed Alanazi |
| author_sort | Muhammad Ibraheem |
| collection | DOAJ |
| description | A topological index (TI) is a molecular descriptor that is applied on a chemical structure to compute the associated numerical value which measures volume, density, boiling point, melting point, surface tension, or solubility of this structure. It is an efficient mathematical method in avoiding laboratory experiments and time-consuming. The forgotten coindex of a structure or (molecular) graph H is defined as the sum of the degrees of all the possible pairs of nonadjacent vertices in H. For D∈S,R,Q,T and the connected graph H, the derived graphs DH are obtained by applying the operations S (subdivided), R (triangle parallel), Q (line superposition), and T (total graph), respectively. Moreover, a derived sum graph (D-sum graph) is obtained by the Cartesian product of the graph H2 with the graph DH1. In this study, we compute forgotten coindex of the D-sum graphs H1+SH2 (S-sum), H1+RH2 (R-sum), H1+QH2 (Q-sum), and H1+TH2 (T-sum) in the form of various indices and coindices of the factor graphs H1 and H2. At the end, we have analyzed our results using numerical tables and graphical behaviour for some particular D-sum graphs. |
| format | Article |
| id | doaj-art-c1cb55a14f74407abced39ad9ee773d4 |
| institution | Kabale University |
| issn | 2090-9063 2090-9071 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Chemistry |
| spelling | doaj-art-c1cb55a14f74407abced39ad9ee773d42025-02-03T05:43:47ZengWileyJournal of Chemistry2090-90632090-90712021-01-01202110.1155/2021/32350683235068Forgotten Coindex for the Derived Sum Graphs under Cartesian ProductMuhammad Ibraheem0Meshari M. Aljohani1Muhammad Javaid2Abdulaziz Mohammed Alanazi3Department of Mathematics, School of Science, University of Management and Technology, Lahore 54770, PakistanDepartment of Chemistry, University of Tabuk, Tabuk, Saudi ArabiaDepartment of Mathematics, School of Science, University of Management and Technology, Lahore 54770, PakistanDepartment of Mathematics, University of Tabuk, Tabuk, Saudi ArabiaA topological index (TI) is a molecular descriptor that is applied on a chemical structure to compute the associated numerical value which measures volume, density, boiling point, melting point, surface tension, or solubility of this structure. It is an efficient mathematical method in avoiding laboratory experiments and time-consuming. The forgotten coindex of a structure or (molecular) graph H is defined as the sum of the degrees of all the possible pairs of nonadjacent vertices in H. For D∈S,R,Q,T and the connected graph H, the derived graphs DH are obtained by applying the operations S (subdivided), R (triangle parallel), Q (line superposition), and T (total graph), respectively. Moreover, a derived sum graph (D-sum graph) is obtained by the Cartesian product of the graph H2 with the graph DH1. In this study, we compute forgotten coindex of the D-sum graphs H1+SH2 (S-sum), H1+RH2 (R-sum), H1+QH2 (Q-sum), and H1+TH2 (T-sum) in the form of various indices and coindices of the factor graphs H1 and H2. At the end, we have analyzed our results using numerical tables and graphical behaviour for some particular D-sum graphs.http://dx.doi.org/10.1155/2021/3235068 |
| spellingShingle | Muhammad Ibraheem Meshari M. Aljohani Muhammad Javaid Abdulaziz Mohammed Alanazi Forgotten Coindex for the Derived Sum Graphs under Cartesian Product Journal of Chemistry |
| title | Forgotten Coindex for the Derived Sum Graphs under Cartesian Product |
| title_full | Forgotten Coindex for the Derived Sum Graphs under Cartesian Product |
| title_fullStr | Forgotten Coindex for the Derived Sum Graphs under Cartesian Product |
| title_full_unstemmed | Forgotten Coindex for the Derived Sum Graphs under Cartesian Product |
| title_short | Forgotten Coindex for the Derived Sum Graphs under Cartesian Product |
| title_sort | forgotten coindex for the derived sum graphs under cartesian product |
| url | http://dx.doi.org/10.1155/2021/3235068 |
| work_keys_str_mv | AT muhammadibraheem forgottencoindexforthederivedsumgraphsundercartesianproduct AT mesharimaljohani forgottencoindexforthederivedsumgraphsundercartesianproduct AT muhammadjavaid forgottencoindexforthederivedsumgraphsundercartesianproduct AT abdulazizmohammedalanazi forgottencoindexforthederivedsumgraphsundercartesianproduct |