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An upper bound on the largest signless Laplacian of an odd unicyclic graphKeywords: Laplacian matrix , signless Laplacian matrix , adjacency matrix , spectral radius , generalized Bethe tree Abstract: We derive an upper bound on the largest signless Laplacian eigenvalue of an odd unicyclic graph. The bound is given in terms of the largest vertex degree and the largest height of the trees obtained removing the edges of the unique cycle in the graph.
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