The First Zagreb Index, the Laplacian Spectral Radius, and Some Hamiltonian Properties of Graphs
Year: 2025
Type: article
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.
Source: Mathematics
DOI: 10.3390/math13172897
Author: Rao Li
Institution: University of South Carolina Aiken
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4414213287