Distribution of signless Laplacian eigenvalues and graph invariants

Abstract

For a simple graph on $n$ vertices, any of its signless Laplacian eigenvalues is in the interval $[0,2n-2]$. In this paper, we give relationships between the number of signless Laplacian eigenvalues in specific intervals in $[0,2n-2]$ and graph invariants including matching number and diameter.