Exact Values of Zagreb Indices for Generalized T-Sum Networks with Lexicographic Product
The use of numerical numbers to represent molecular networks plays a crucial role in the study of physicochemical and structural properties of the chemical compounds. For some integer k and a network G, the networks SkG and RkG are its derived networks called as generalized subdivided and generalize...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/4041290 |
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| author | Jia-Bao Liu Sana Akram Muhammad Javaid Zhi-Ba Peng |
| author_facet | Jia-Bao Liu Sana Akram Muhammad Javaid Zhi-Ba Peng |
| author_sort | Jia-Bao Liu |
| collection | DOAJ |
| description | The use of numerical numbers to represent molecular networks plays a crucial role in the study of physicochemical and structural properties of the chemical compounds. For some integer k and a network G, the networks SkG and RkG are its derived networks called as generalized subdivided and generalized semitotal point networks, where Sk and Rk are generalized subdivision and generalized semitotal point operations, respectively. Moreover, for two connected networks, G1 and G2, G1G2Sk and G1G2Rk are T-sum networks which are obtained by the lexicographic product of TG1 and G2, respectively, where TεSk,Rk. In this paper, for the integral value k≥1, we find exact values of the first and second Zagreb indices for generalized T-sum networks. Furthermore, the obtained findings are general extensions of some known results for only k=1. At the end, a comparison among the different generalized T-sum networks with respect to first and second Zagreb indices is also included. |
| format | Article |
| id | doaj-art-ec64f90f7feb4f9d9e51359f51b58b67 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-ec64f90f7feb4f9d9e51359f51b58b672025-02-03T07:23:55ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/40412904041290Exact Values of Zagreb Indices for Generalized T-Sum Networks with Lexicographic ProductJia-Bao Liu0Sana Akram1Muhammad Javaid2Zhi-Ba Peng3School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, ChinaDepartment of Mathematics, School of Science, University of Management and Technology, Lahore, PakistanDepartment of Mathematics, School of Science, University of Management and Technology, Lahore, PakistanSchool of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, ChinaThe use of numerical numbers to represent molecular networks plays a crucial role in the study of physicochemical and structural properties of the chemical compounds. For some integer k and a network G, the networks SkG and RkG are its derived networks called as generalized subdivided and generalized semitotal point networks, where Sk and Rk are generalized subdivision and generalized semitotal point operations, respectively. Moreover, for two connected networks, G1 and G2, G1G2Sk and G1G2Rk are T-sum networks which are obtained by the lexicographic product of TG1 and G2, respectively, where TεSk,Rk. In this paper, for the integral value k≥1, we find exact values of the first and second Zagreb indices for generalized T-sum networks. Furthermore, the obtained findings are general extensions of some known results for only k=1. At the end, a comparison among the different generalized T-sum networks with respect to first and second Zagreb indices is also included.http://dx.doi.org/10.1155/2021/4041290 |
| spellingShingle | Jia-Bao Liu Sana Akram Muhammad Javaid Zhi-Ba Peng Exact Values of Zagreb Indices for Generalized T-Sum Networks with Lexicographic Product Journal of Mathematics |
| title | Exact Values of Zagreb Indices for Generalized T-Sum Networks with Lexicographic Product |
| title_full | Exact Values of Zagreb Indices for Generalized T-Sum Networks with Lexicographic Product |
| title_fullStr | Exact Values of Zagreb Indices for Generalized T-Sum Networks with Lexicographic Product |
| title_full_unstemmed | Exact Values of Zagreb Indices for Generalized T-Sum Networks with Lexicographic Product |
| title_short | Exact Values of Zagreb Indices for Generalized T-Sum Networks with Lexicographic Product |
| title_sort | exact values of zagreb indices for generalized t sum networks with lexicographic product |
| url | http://dx.doi.org/10.1155/2021/4041290 |
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