Abstract
We determine the second to fourth largest (resp. the second smallest) signless Laplacian spectral radii and the second to fourth largest signless Laplacian spreads together with the corresponding graphs in the class of unicyclic graphs with n vertices. Moreover, we prove that one class of unicyclic graphs are determined by their signless Laplacian spectra.
Highlights
Throughout the paper, G V, E is an undirected simple graph with n vertices and m edges
Let Un be the class of unicyclic graphs with n vertices
The largest signless Laplacian spectral radius and the largest signless Laplacian spread among the class of unicyclic graphs with n vertices were determined in 6 and 1, respectively
Summary
Throughout the paper, G V, E is an undirected simple graph with n vertices and m edges. Let Un be the class of unicyclic graphs with n vertices. The largest signless Laplacian spectral radius and the largest signless Laplacian spread among the class of unicyclic graphs with n vertices were determined in 6 and 1 , respectively. The smallest signless Laplacian spectral radius among the class of unicyclic graphs with n vertices was determined in 7. We will determine the second to fourth largest and the second smallest signless Laplacian spectral radii together with the corresponding graphs in the class of unicyclic graphs with n vertices. We indentify the second to fourth largest signless Laplacian spreads together with the corresponding graphs in the class of unicyclic graphs with n vertices. In the end of this paper, we will prove that a class of unicyclic graphs are determined by their signless Laplacian spectra
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