  The best degree-based upper bound for the spectral radius is due to Liu and
Weng. This paper begins by demonstrating that a (forgotten) upper bound for the
spectral radius dating from 1983 is equivalent to their much more recent bound.
This bound is then used to compare lower bounds for the clique number. A series
of sharp upper bounds for the signless Laplacian spectral radius is then
proposed as another application. Finally a new lower bound for generalised
r-partite graphs is proved, by extending a result due to Erdos.
