Distance (Signless) Laplacian Eigenvalues of $k$-uniform Hypergraphs

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.