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.