Some Inequalities between General Randić-Type Graph Invariants
The Randić-type graph invariants are extensively investigated vertex-degree-based topological indices and have gained much prominence in recent years. The general Randić and zeroth-order general Randić indices are Randić-type graph invariants and are defined for a graph G with vertex set V as RαG=∑υ...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/8204742 |
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| _version_ | 1832558488551686144 |
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| author | Imran Nadeem Saba Siddique Yilun Shang |
| author_facet | Imran Nadeem Saba Siddique Yilun Shang |
| author_sort | Imran Nadeem |
| collection | DOAJ |
| description | The Randić-type graph invariants are extensively investigated vertex-degree-based topological indices and have gained much prominence in recent years. The general Randić and zeroth-order general Randić indices are Randić-type graph invariants and are defined for a graph G with vertex set V as RαG=∑υi∼υjdidjα and QαG=∑vi∈Vdiα, respectively, where α is an arbitrary real number, di denotes the degree of a vertex υi, and υi∼υj represents the adjacency of vertices υi and υj in G. Establishing relationships between two topological indices holds significant importance for researchers. Some implicit inequality relationships between Rα and Qα have been derived so far. In this paper, we establish explicit inequality relationships between Rα and Qα. Also, we determine linear inequality relationships between these graph invariants. Moreover, we obtain some new inequalities for various vertex-degree-based topological indices by the appropriate choice of α. |
| format | Article |
| id | doaj-art-eb09c3b46ca84623ae8cef7c7d1bc642 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-eb09c3b46ca84623ae8cef7c7d1bc6422025-02-03T01:32:20ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/8204742Some Inequalities between General Randić-Type Graph InvariantsImran Nadeem0Saba Siddique1Yilun Shang2Higher Education DepartmentDepartment of MathematicsDepartment of Computer and Information SciencesThe Randić-type graph invariants are extensively investigated vertex-degree-based topological indices and have gained much prominence in recent years. The general Randić and zeroth-order general Randić indices are Randić-type graph invariants and are defined for a graph G with vertex set V as RαG=∑υi∼υjdidjα and QαG=∑vi∈Vdiα, respectively, where α is an arbitrary real number, di denotes the degree of a vertex υi, and υi∼υj represents the adjacency of vertices υi and υj in G. Establishing relationships between two topological indices holds significant importance for researchers. Some implicit inequality relationships between Rα and Qα have been derived so far. In this paper, we establish explicit inequality relationships between Rα and Qα. Also, we determine linear inequality relationships between these graph invariants. Moreover, we obtain some new inequalities for various vertex-degree-based topological indices by the appropriate choice of α.http://dx.doi.org/10.1155/2024/8204742 |
| spellingShingle | Imran Nadeem Saba Siddique Yilun Shang Some Inequalities between General Randić-Type Graph Invariants Journal of Mathematics |
| title | Some Inequalities between General Randić-Type Graph Invariants |
| title_full | Some Inequalities between General Randić-Type Graph Invariants |
| title_fullStr | Some Inequalities between General Randić-Type Graph Invariants |
| title_full_unstemmed | Some Inequalities between General Randić-Type Graph Invariants |
| title_short | Some Inequalities between General Randić-Type Graph Invariants |
| title_sort | some inequalities between general randic type graph invariants |
| url | http://dx.doi.org/10.1155/2024/8204742 |
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