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Bosch, P., Rodríguez, J.M., Sigarreta, J.M. and Tourís, E. (2024) Some New Milne-Type Inequalities. Journal of Inequalities and Applications, 2024, Article No. 106.
https://doi.org/10.1186/s13660-024-03184-4

has been cited by the following article:

• TITLE: The First Zagreb Index, the Independence Number and Some Hamiltonian Properties of Graphs

  AUTHORS: Rao Li

  KEYWORDS: The First Zagreb Index, The Independence Number, Hamiltonian Graph, Traceable Graph

  JOURNAL NAME: Open Journal of Discrete Mathematics, Vol.15 No.4, September 5, 2025

  ABSTRACT: Let G=( V,E ) be a graph. The first Zagreb index of a graph G is defined as ∑ u∈V d G 2 ( u ) , where d G ( u ) is the degree of vertex u in G . In this paper, we obtain two lower bounds involving the independence number for the first Zagreb index of a graph. We also characterize the graphs achieving the bounds. We further present sufficient conditions based on the first Zagreb index for Hamiltonian graphs and traceable graphs.