On the Minimum General Sum-Connectivity of Trees of Fixed Order and Pendent Vertices

Abeer M. Albalahi, Akbar Ali and Xian-Ming Gu

Journal of Mathematics, 2022, vol. 2022, 1-4

Abstract: 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.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:8567266

DOI: 10.1155/2022/8567266

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