For large orders, the unique extremal graphs for the signless Laplacian spectral radius among K2,t-minor free and K3,3-minor free graphs are F2,t(n) and F3,3(n), respectively.
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On the signless Laplacian spectral radius of $K_{s,t}$-minor free graphs
For large orders, the unique extremal graphs for the signless Laplacian spectral radius among K2,t-minor free and K3,3-minor free graphs are F2,t(n) and F3,3(n), respectively.