Abstract

The distance (signless) Laplacian eigenvalues of a connected hypergraph are the eigenvalues of its distance (signless) Laplacian matrix. For all $n$-vertex $k$-uniform hypertrees, we determine the $k$-uniform hypertree with minimum second largest distance (signless) Laplacian eigenvalue. For all $n$-vertex $k$-uniform unicyclic hypergraphs, we obtain the $k$-uniform unicyclic hypergraph with minimum largest distance (signless) Laplacian eigenvalue, and the $k$-uniform unicyclic hypergraph with minimum second largest distance Laplacian eigenvalue.

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