In structural graph theory,significant advancements have been made in characterizing the Hamiltonian nature of the graphs using the spectral radius.However,there remains a lack of research on the spectral radius of Hamilton graphs.Therefore,in this article,based on the concept of a quadricyclic Hamilton graphs and the relationship between the spectral pa-rameters and structural parameters of the graphs,we determine the structure of graphs with maximum signless Laplacian spec-tral radius in the class of quadricyclic Hamiltonian graph with maximum degrees 3 and 5,respectively.
维普
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