For large n, the maximum signless Laplacian spectral radius among n-vertex r-dimensional pure simplicial complexes without r-dimensional wheels is attained by specific extremal complexes, generalizing graph results and providing a spectral analogue of the Sós-Erdős-Brown theorem for r=2.
Eckmann, Harmonische Funktionen und Randwertaufgaben in einem Komplex,Comment
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Signless Laplacian spectral radius of simplicial complexes without $r$-dimensional wheels
For large n, the maximum signless Laplacian spectral radius among n-vertex r-dimensional pure simplicial complexes without r-dimensional wheels is attained by specific extremal complexes, generalizing graph results and providing a spectral analogue of the Sós-Erdős-Brown theorem for r=2.