On the Minimum General Sum-Connectivity of Trees of Fixed Order and Pendent Vertices
For a graph G, its general sum-connectivity is usually denoted by χαG and is defined as the sum of the numbers dGu+dGvα over all edges uv of G, where dGu,dGv represent degrees of the vertices u,v, respectively, and α is a real number. This paper addresses the problem of finding graphs possessing the...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/8567266 |
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| author | Abeer M. Albalahi Akbar Ali |
| author_facet | Abeer M. Albalahi Akbar Ali |
| author_sort | Abeer M. Albalahi |
| collection | DOAJ |
| description | For a graph G, its general sum-connectivity is usually denoted by χαG and is defined as the sum of the numbers dGu+dGvα over all edges uv of G, where dGu,dGv represent degrees of the vertices u,v, respectively, and α is a real number. This paper addresses the problem of finding graphs possessing the minimum χα value over the class of all trees with a fixed order n and fixed number of pendent vertices n1 for α>1. This problem is solved here for the case when 4≤n1≤n+5/3 and α>1, by deriving a lower bound on χα for trees in terms of their orders and number of pendent vertices. |
| format | Article |
| id | doaj-art-3242a5b2ea9e4d07b7912357bae0c530 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-3242a5b2ea9e4d07b7912357bae0c5302025-02-03T05:53:29ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/8567266On the Minimum General Sum-Connectivity of Trees of Fixed Order and Pendent VerticesAbeer M. Albalahi0Akbar Ali1Department of MathematicsDepartment of MathematicsFor a graph G, its general sum-connectivity is usually denoted by χαG and is defined as the sum of the numbers dGu+dGvα over all edges uv of G, where dGu,dGv represent degrees of the vertices u,v, respectively, and α is a real number. This paper addresses the problem of finding graphs possessing the minimum χα value over the class of all trees with a fixed order n and fixed number of pendent vertices n1 for α>1. This problem is solved here for the case when 4≤n1≤n+5/3 and α>1, by deriving a lower bound on χα for trees in terms of their orders and number of pendent vertices.http://dx.doi.org/10.1155/2022/8567266 |
| spellingShingle | Abeer M. Albalahi Akbar Ali On the Minimum General Sum-Connectivity of Trees of Fixed Order and Pendent Vertices Journal of Mathematics |
| title | On the Minimum General Sum-Connectivity of Trees of Fixed Order and Pendent Vertices |
| title_full | On the Minimum General Sum-Connectivity of Trees of Fixed Order and Pendent Vertices |
| title_fullStr | On the Minimum General Sum-Connectivity of Trees of Fixed Order and Pendent Vertices |
| title_full_unstemmed | On the Minimum General Sum-Connectivity of Trees of Fixed Order and Pendent Vertices |
| title_short | On the Minimum General Sum-Connectivity of Trees of Fixed Order and Pendent Vertices |
| title_sort | on the minimum general sum connectivity of trees of fixed order and pendent vertices |
| url | http://dx.doi.org/10.1155/2022/8567266 |
| work_keys_str_mv | AT abeermalbalahi ontheminimumgeneralsumconnectivityoftreesoffixedorderandpendentvertices AT akbarali ontheminimumgeneralsumconnectivityoftreesoffixedorderandpendentvertices |