  Exclusive measurements of high energy $\gamma$-rays are performed in $\rm
^{124}Ba$ and $\rm ^{136}Ba$ at the same excitation energy ($\sim$ 49 MeV), to
study properties of the giant dipole resonance (GDR) over a wider $N/Z$ range.
The high energy $\gamma$-rays are measured in coincidence with the multiplicity
of low energy $\gamma$-rays to disentangle the effect of temperature ($T$) and
angular momentum ($J$). The GDR parameters are extracted employing a simulated
Monte Carlo statistical model analysis. The observed $\gamma$-ray spectra of
$\rm ^{124}Ba$ can be explained with prolate deformation, whereas a single
component Lorentzian function which corresponds to a spherical shape could
explain the $\gamma$-ray spectra from $\rm ^{136}Ba$. The observed GDR width in
$\rm ^{136}Ba$ is narrower compared to that of $\rm ^{124}Ba$.
  The statistical model best fit GDR cross sections are found to be in good
agreement with the thermal shape fluctuation model (TSFM) calculations.
Further, it is shown that the variation of GDR width with $T$ is well
reproduced by the TSFM calculations over the temperature range of 1.1--1.7MeV.
