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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-4785 |