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

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  • Abeer M. Albalahi
  • Akbar Ali
  • Xian-Ming Gu

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.

Suggested Citation

  • Abeer M. Albalahi & Akbar Ali & Xian-Ming Gu, 2022. "On the Minimum General Sum-Connectivity of Trees of Fixed Order and Pendent Vertices," Journal of Mathematics, Hindawi, vol. 2022, pages 1-4, June.
    • Handle: RePEc:hin:jjmath:8567266
    DOI: 10.1155/2022/8567266
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