  The purpose of this paper is to highlight the role played by the anti-regular
graph within the class of threshold graphs. Using the fact that every threshold
graph contains a maximal anti-regular graph, we show that some known results,
and new ones, on the spectral properties of threshold graphs can be deduced
from (i) the known results on the eigenvalues of anti-regular graphs, (ii) the
subgraph structure of threshold graphs, and (iii) eigenvalue interlacing. In
particular, we prove a strengthened version of the recently proved fact that no
threshold graph contains an eigenvalue in the interval $\Omega =
[\frac{-1-\sqrt{2}}{2},\frac{-1+\sqrt{2}}{2}]$, except possibly the trivial
eigenvalues $-1$ and/or $0$, determine the inertia of a threshold graph, and
give partial results on a conjecture regarding the optimality of the
non-trivial eigenvalues of an anti-regular graph within the class of threshold
graphs.
