  We investigate a kinematic scaling relation between the baryonic mass and the
flat velocity dispersion, i.e. mass-velocity dispersion relation (MVDR), from
the brightest cluster galaxies (BCGs) to the galaxy clusters. In our studies,
the baryonic mass of BCGs is mainly estimated by photometry. The velocity
dispersion profiles are explored with the integrated field unit (IFU) by
Mapping Nearby Galaxies at Apache Point Observatory (MaNGA). For the first
time, we reveal two significant results with 54 MaNGA BCGs: (1) the flat
velocity dispersion profiles; (2) a tight empirical relation on the BCG-cluster
scale together with cluster samples, i.e., MVDR,
$\log(M_\mathrm{bar}/M_\odot)=4.1^{+0.1}_{-0.1}\log(\sigma_{\mathrm{los}}/\mathrm{km}\,\mathrm{s}^{-1})+1.6^{+0.3}_{-0.3}$,
with a tiny lognormal intrinsic scatter of $10^{+2}_{-1}\%$. This slope is
identical to the acceleration relation in galaxy clusters, which is reminiscent
of the spiral galaxies, albeit at a larger characteristic acceleration scale.
The residuals of the MVDR represent a Gaussian distribution, displaying no
correlations with four properties: baryonic mass, scale length, surface
density, and redshift. Notably, the MVDR on the BCG-cluster scale provides a
strict test, which disfavors the general prediction of the slope of three in
the dark matter model.
