On Least Distance Eigenvalue of Uniform Hypergraphs

Abstract

For $k \geq 2$, we determine the connected $k$-uniform hypergraphs with least distance eigenvalues in $((1-\sqrt{33})/2,0)$, the $k$-uniform hypertrees with least distance eigenvalues in $[-2k,0)$, and the $k$-uniform unicyclic hypergraphs with least distance eigenvalues in $(-k+1-\sqrt{(k-1)(k-2)},0)$, respectively, and determine the $k$-uniform hypergraphs (hypertrees, respectively) with minimum distance spread.