Determination of dynamical ages of open clusters through the A$^+$
  parameter -- I
  The sedimentation level of blue straggler stars (BSS) has been shown to be a
great tool to investigate the dynamical states of globular clusters (GCs). The
area enclosed between the cumulative radial distributions of BSS and a
reference population up to the half-mass radius of the clusters,
$A^+_{\mathrm{rh}}$, is known to be a measure of the sedimentation of BSS in
GCs. In this work, we calculate $A^+_{\mathrm{rh}}$ for 11 open clusters (OCs)
using a combined list of main-sequence turn-off stars, sub-giant branch stars,
and red-giant branch stars as reference population. The BSS, the reference
populations, and the cluster members are identified using the proper motions
and parallaxes from the Gaia DR2 data. In a subset of clusters, the BSS are
confirmed cluster members on the basis of radial velocity information available
in the literature. Using the Pearson and Spearman rank correlation
coefficients, we find weak correlations between the estimated values of
$A^+_{\mathrm{rh}}$ and other markers of dynamical ages of the clusters, i.e.,
the number of central relaxations a cluster has experienced since its
formation, and the structural parameters of the clusters. Based on statistical
tests, we find that these correlations are similar to the corresponding
correlations among the less evolved GCs, albeit within large errors.
