The First Zagreb Index, the Laplacian Spectral Radius, and Some Hamiltonian Properties of Graphs

Rao Li ()
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Rao Li: Department of Computer Science, Engineering and Mathematics, University of South Carolina Aiken, Aiken, SC 29801, USA

Mathematics, 2025, vol. 13, issue 17, 1-15

Abstract: The first Zagreb index of a graph G is defined as the sum of the squares of the degrees of all the vertices in G . The Laplacian spectral radius of a graph G is defined as the largest eigenvalue of the Laplacian matrix of the graph G . In this paper, we first establish inequalities on the first Zagreb index and the Laplacian spectral radius of a graph. Using the ideas of proving the inequalities, we present sufficient conditions involving the first Zagreb index and the Laplacian spectral radius for some Hamiltonian properties of graphs.

Keywords: first Zagreb index; Laplacian spectral radius; Hamiltonian graph; traceable graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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