Computing Analysis of Connection-Based Indices and Coindices for Product of Molecular Networks
Gutman and Trinajstić (1972) defined the connection-number based Zagreb indices, where connection number is degree of a vertex at distance two, in order to find the electron energy of alternant hydrocarbons. These indices remain symmetric for the isomorphic (molecular) networks. For the prediction o...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-08-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/12/8/1320 |
| _version_ | 1797559758100627456 |
|---|---|
| author | Usman Ali Muhammad Javaid Abdulaziz Mohammed Alanazi |
| author_facet | Usman Ali Muhammad Javaid Abdulaziz Mohammed Alanazi |
| author_sort | Usman Ali |
| collection | DOAJ |
| description | Gutman and Trinajstić (1972) defined the connection-number based Zagreb indices, where connection number is degree of a vertex at distance two, in order to find the electron energy of alternant hydrocarbons. These indices remain symmetric for the isomorphic (molecular) networks. For the prediction of physicochemical and symmetrical properties of octane isomers, these indices are restudied in 2018. In this paper, first and second Zagreb connection coindices are defined and obtained in the form of upper bounds for the resultant networks in the terms of different indices of their factor networks, where resultant networks are obtained from two networks by the product-related operations, such as cartesian, corona, and lexicographic. For the molecular networks linear polynomial chain, carbon nanotube, alkane, cycloalkane, fence, and closed fence, first and second Zagreb connection coindices are computed in the consequence of the obtained results. An analysis of Zagreb connection indices and coindices on the aforesaid molecular networks is also included with the help of their numerical values and graphical presentations that shows the symmetric behaviour of these indices and coindices with in certain intervals of order and size of the under study (molecular) networks. |
| first_indexed | 2024-03-10T17:49:52Z |
| format | Article |
| id | doaj.art-618b7f01231a45e6a38a008526908430 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T17:49:52Z |
| publishDate | 2020-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-618b7f01231a45e6a38a0085269084302023-11-20T09:23:50ZengMDPI AGSymmetry2073-89942020-08-01128132010.3390/sym12081320Computing Analysis of Connection-Based Indices and Coindices for Product of Molecular NetworksUsman Ali0Muhammad Javaid1Abdulaziz Mohammed Alanazi2Department of Mathematics, School of Science, University of Management and Technology, Lahore 54770, PakistanDepartment of Mathematics, School of Science, University of Management and Technology, Lahore 54770, PakistanDepartment of Mathematics, University of Tabuk, Tabuk 71491, Saudi ArabiaGutman and Trinajstić (1972) defined the connection-number based Zagreb indices, where connection number is degree of a vertex at distance two, in order to find the electron energy of alternant hydrocarbons. These indices remain symmetric for the isomorphic (molecular) networks. For the prediction of physicochemical and symmetrical properties of octane isomers, these indices are restudied in 2018. In this paper, first and second Zagreb connection coindices are defined and obtained in the form of upper bounds for the resultant networks in the terms of different indices of their factor networks, where resultant networks are obtained from two networks by the product-related operations, such as cartesian, corona, and lexicographic. For the molecular networks linear polynomial chain, carbon nanotube, alkane, cycloalkane, fence, and closed fence, first and second Zagreb connection coindices are computed in the consequence of the obtained results. An analysis of Zagreb connection indices and coindices on the aforesaid molecular networks is also included with the help of their numerical values and graphical presentations that shows the symmetric behaviour of these indices and coindices with in certain intervals of order and size of the under study (molecular) networks.https://www.mdpi.com/2073-8994/12/8/1320connection numberZagreb indicescoindicesproduct of networks |
| spellingShingle | Usman Ali Muhammad Javaid Abdulaziz Mohammed Alanazi Computing Analysis of Connection-Based Indices and Coindices for Product of Molecular Networks Symmetry connection number Zagreb indices coindices product of networks |
| title | Computing Analysis of Connection-Based Indices and Coindices for Product of Molecular Networks |
| title_full | Computing Analysis of Connection-Based Indices and Coindices for Product of Molecular Networks |
| title_fullStr | Computing Analysis of Connection-Based Indices and Coindices for Product of Molecular Networks |
| title_full_unstemmed | Computing Analysis of Connection-Based Indices and Coindices for Product of Molecular Networks |
| title_short | Computing Analysis of Connection-Based Indices and Coindices for Product of Molecular Networks |
| title_sort | computing analysis of connection based indices and coindices for product of molecular networks |
| topic | connection number Zagreb indices coindices product of networks |
| url | https://www.mdpi.com/2073-8994/12/8/1320 |
| work_keys_str_mv | AT usmanali computinganalysisofconnectionbasedindicesandcoindicesforproductofmolecularnetworks AT muhammadjavaid computinganalysisofconnectionbasedindicesandcoindicesforproductofmolecularnetworks AT abdulazizmohammedalanazi computinganalysisofconnectionbasedindicesandcoindicesforproductofmolecularnetworks |