A connected graph G is a cactus if any two of its cycles have at most one common vertex. Let ℓ m n be the set of cacti on n vertices with matching number m. S.C. Li and M.J. Zhang determined the unique graph with the maximum signless Laplacian spectral radius among all cacti in ℓ m n with n = 2m. In this paper, we characterize the case n ≥ 2m+1. This confirms the conjecture of Li and Zhang (S.C. Li, M.J. Zhang, On the signless Laplacian index of cacti with a given number of pendant vetices, Linear Algebra Appl. 436, 2012,[4400][4401][4402][4403][4404][4405][4406][4407][4408][4409][4410][4411]. Further, we characterize the unique graph with the maximum signless Laplacian spectral radius among all cacti on n vertices.
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