First General Zagreb Index of Generalized F-sum Graphs
The first general Zagreb (FGZ) index (also known as the general zeroth-order Randić index) of a graph G can be defined as MγG=∑uv∈EGdGγ−1u+dGγ−1v, where γ is a real number. As MγG is equal to the order and size of G when γ=0 and γ=1, respectively, γ is usually assumed to be different from 0 to 1. In...
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| Format: | Article |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/2954975 |
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| author | H. M. Awais Muhammad Javaid Akbar Ali |
| author_facet | H. M. Awais Muhammad Javaid Akbar Ali |
| author_sort | H. M. Awais |
| collection | DOAJ |
| description | The first general Zagreb (FGZ) index (also known as the general zeroth-order Randić index) of a graph G can be defined as MγG=∑uv∈EGdGγ−1u+dGγ−1v, where γ is a real number. As MγG is equal to the order and size of G when γ=0 and γ=1, respectively, γ is usually assumed to be different from 0 to 1. In this paper, for every integer γ≥2, the FGZ index Mγ is computed for the generalized F-sums graphs which are obtained by applying the different operations of subdivision and Cartesian product. The obtained results can be considered as the generalizations of the results appeared in (IEEE Access; 7 (2019) 47494–47502) and (IEEE Access 7 (2019) 105479–105488). |
| format | Article |
| id | doaj-art-1b80ef5aba834f939a1868ddf5dd58d2 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-1b80ef5aba834f939a1868ddf5dd58d22025-02-03T01:25:41ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/29549752954975First General Zagreb Index of Generalized F-sum GraphsH. M. Awais0Muhammad Javaid1Akbar Ali2Department of Mathematics, School of Science, University of Management and Technology, Lahore, PakistanDepartment of Mathematics, School of Science, University of Management and Technology, Lahore, PakistanDepartment of Mathematics, Faculty of Science, University of Ha’il, Ha’il, Saudi ArabiaThe first general Zagreb (FGZ) index (also known as the general zeroth-order Randić index) of a graph G can be defined as MγG=∑uv∈EGdGγ−1u+dGγ−1v, where γ is a real number. As MγG is equal to the order and size of G when γ=0 and γ=1, respectively, γ is usually assumed to be different from 0 to 1. In this paper, for every integer γ≥2, the FGZ index Mγ is computed for the generalized F-sums graphs which are obtained by applying the different operations of subdivision and Cartesian product. The obtained results can be considered as the generalizations of the results appeared in (IEEE Access; 7 (2019) 47494–47502) and (IEEE Access 7 (2019) 105479–105488).http://dx.doi.org/10.1155/2020/2954975 |
| spellingShingle | H. M. Awais Muhammad Javaid Akbar Ali First General Zagreb Index of Generalized F-sum Graphs Discrete Dynamics in Nature and Society |
| title | First General Zagreb Index of Generalized F-sum Graphs |
| title_full | First General Zagreb Index of Generalized F-sum Graphs |
| title_fullStr | First General Zagreb Index of Generalized F-sum Graphs |
| title_full_unstemmed | First General Zagreb Index of Generalized F-sum Graphs |
| title_short | First General Zagreb Index of Generalized F-sum Graphs |
| title_sort | first general zagreb index of generalized f sum graphs |
| url | http://dx.doi.org/10.1155/2020/2954975 |
| work_keys_str_mv | AT hmawais firstgeneralzagrebindexofgeneralizedfsumgraphs AT muhammadjavaid firstgeneralzagrebindexofgeneralizedfsumgraphs AT akbarali firstgeneralzagrebindexofgeneralizedfsumgraphs |