  Stellar mass $M$, radius $R$, and gravity $g$ are important basic parameters
in stellar physics. Accurate values for these parameters can be obtained from
the gravitational interaction between stars in multiple systems or from
asteroseismology. Stars in a cluster are thought to be formed coevally from the
same interstellar cloud of gas and dust. The cluster members are therefore
expected to have some properties in common. These common properties strengthen
our ability to constrain stellar models and asteroseismically derived $M$, $R$
and $g$ when tested against an ensemble of cluster stars. Here we derive new
scaling relations based on a relation for stars on the Hayashi track
($\sqrt{T_{\rm eff}} \sim g^pR^q$) to determine the masses and metallicities of
red giant branch stars in open clusters NGC 6791 and NGC 6819 from the global
oscillation parameters $\Delta\nu$ (the large frequency separation) and
$\nu_{\rm max}$ (frequency of maximum oscillation power). The $\Delta\nu$ and
$\nu_{\rm max}$ values are derived from \kepler\ observations. From the
analysis of these new relations we derive: (1) direct observational evidence
that the masses of red giant branch stars in a cluster are the same within
their uncertainties, (2) new methods to derive $M$ and $z$ of the cluster in a
self consistent way from $\Delta\nu$ and $\nu_{\rm max}$, with lower intrinsic
uncertainties, (3) the mass dependence in the $\Delta\nu$ - $\nu_{\rm max}$
relation for red giant branch stars.
