  Microscopic relaxation timescales are estimated from the autocorrelation
functions obtained by dynamic light scattering experiments for Laponite
suspensions with different concentrations ($C_{L}$), added salt concentrations
($C_{S}$) and temperatures ($T$). It has been shown in an earlier work [Soft
Matter, 10, 3292-3300 (2014)] that the evolutions of relaxation timescales of
colloidal glasses can be compared with molecular glass formers by mapping the
waiting time ($t_{w}$) of the former with the inverse of thermodynamic
temperature ($1/T$) of the latter. In this work, the fragility parameter $D$,
which signifies the deviation from Arrhenius behavior, is obtained from fits to
the time evolutions of the structural relaxation timescales. For the Laponite
suspensions studied in this work, $D$ is seen to be independent of $C_{L}$ and
$C_{S}$, but is weakly dependent on $T$. Interestingly, the behavior of $D$
corroborates the behavior of fragility in molecular glass formers with respect
to equivalent variables. Furthermore, the stretching exponent $\beta$, which
quantifies the width $w$ of the spectrum of structural relaxation timescales is
seen to depend on $t_{w}$. A hypothetical Kauzmann time $t_{k}$, analogous to
the Kauzmann temperature for molecular glasses, is defined as the timescale at
which $w$ diverges. Corresponding to the Vogel temperature defined for
molecular glasses, a hypothetical Vogel time $t^{\infty}_{\alpha}$ is also
defined as the time at which the structural relaxation time diverges.
Interestingly, a correlation is observed between $t_{k}$ and
$t^{\infty}_{\alpha}$, which is remarkably similar to that known for fragile
molecular glass formers. A coupling model that accounts for the
$t_{w}$-dependence of the stretching exponent is used to analyse and explain
the observed correlation between $t_{k}$ and $t^{\infty}_{\alpha}$.
