On-Bond Incident Degree Indices of Square-Hexagonal Chains
For a graph G, its bond incident degree (BID) index is defined as the sum of the contributions fdu,dv over all edges uv of G, where dw denotes the degree of a vertex w of G and f is a real-valued symmetric function. If fdu,dv=du+dv or dudv, then the corresponding BID index is known as the first Zagr...
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| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/1864828 |
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| author | Tariq A. Alraqad Hicham Saber Akbar Ali Jaya Percival Mazorodze |
| author_facet | Tariq A. Alraqad Hicham Saber Akbar Ali Jaya Percival Mazorodze |
| author_sort | Tariq A. Alraqad |
| collection | DOAJ |
| description | For a graph G, its bond incident degree (BID) index is defined as the sum of the contributions fdu,dv over all edges uv of G, where dw denotes the degree of a vertex w of G and f is a real-valued symmetric function. If fdu,dv=du+dv or dudv, then the corresponding BID index is known as the first Zagreb index M1 or the second Zagreb index M2, respectively. The class of square-hexagonal chains is a subclass of the class of molecular graphs of minimum degree 2. (Formal definition of a square-hexagonal chain is given in the Introduction section). The present study is motivated from the paper (C. Xiao, H. Chen, Discrete Math. 339 (2016) 506–510) concerning square-hexagonal chains. In the present paper, a general expression for calculating any BID index of square-hexagonal chains is derived. The chains attaining the maximum or minimum values of M1 and M2 are also characterized from the class of all square-hexagonal chains having a fixed number of polygons. |
| format | Article |
| id | doaj-art-e77499a669ce4be793221bc835f6e3c3 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-e77499a669ce4be793221bc835f6e3c32025-02-03T07:25:03ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/1864828On-Bond Incident Degree Indices of Square-Hexagonal ChainsTariq A. Alraqad0Hicham Saber1Akbar Ali2Jaya Percival Mazorodze3Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsFor a graph G, its bond incident degree (BID) index is defined as the sum of the contributions fdu,dv over all edges uv of G, where dw denotes the degree of a vertex w of G and f is a real-valued symmetric function. If fdu,dv=du+dv or dudv, then the corresponding BID index is known as the first Zagreb index M1 or the second Zagreb index M2, respectively. The class of square-hexagonal chains is a subclass of the class of molecular graphs of minimum degree 2. (Formal definition of a square-hexagonal chain is given in the Introduction section). The present study is motivated from the paper (C. Xiao, H. Chen, Discrete Math. 339 (2016) 506–510) concerning square-hexagonal chains. In the present paper, a general expression for calculating any BID index of square-hexagonal chains is derived. The chains attaining the maximum or minimum values of M1 and M2 are also characterized from the class of all square-hexagonal chains having a fixed number of polygons.http://dx.doi.org/10.1155/2022/1864828 |
| spellingShingle | Tariq A. Alraqad Hicham Saber Akbar Ali Jaya Percival Mazorodze On-Bond Incident Degree Indices of Square-Hexagonal Chains Journal of Mathematics |
| title | On-Bond Incident Degree Indices of Square-Hexagonal Chains |
| title_full | On-Bond Incident Degree Indices of Square-Hexagonal Chains |
| title_fullStr | On-Bond Incident Degree Indices of Square-Hexagonal Chains |
| title_full_unstemmed | On-Bond Incident Degree Indices of Square-Hexagonal Chains |
| title_short | On-Bond Incident Degree Indices of Square-Hexagonal Chains |
| title_sort | on bond incident degree indices of square hexagonal chains |
| url | http://dx.doi.org/10.1155/2022/1864828 |
| work_keys_str_mv | AT tariqaalraqad onbondincidentdegreeindicesofsquarehexagonalchains AT hichamsaber onbondincidentdegreeindicesofsquarehexagonalchains AT akbarali onbondincidentdegreeindicesofsquarehexagonalchains AT jayapercivalmazorodze onbondincidentdegreeindicesofsquarehexagonalchains |