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The First Zagreb Index, the Independence Number and Some Hamiltonian Properties of Graphs
Department of Computer Science, Engineering and Mathematics, University of South Carolina Aiken, Aiken, SC 29801, USA
- 1 Department of Computer Science, Engineering and Mathematics, University of South Carolina Aiken, Aiken, SC 29801, USA
Open Journal of Discrete Mathematics·Volume 15 (2025)·Pages 92–99·Published 27 August 2025·DOI10.4236/ojdm.2025.154007
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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.
KeywordsThe First Zagreb IndexThe Independence NumberHamiltonian GraphTraceable Graph
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