  Neutron deficient nuclei from $^{74}$Se$-^{196}$Hg are thought to be produced
by $\gamma$-induced reactions ($\gamma$,n), ($\gamma$,p) and ($\gamma,\alpha$)
processes. The relatively high abundance of $^{113}$In odd A $p$-nuclei has
inspired to study its production processes. As reaction with $\gamma$-beam is
difficult to perform in the laboratory, $\gamma$-induced reaction rate is
calculated from the inverse reaction data employing reciprocity theorem.
Stacked foil activation method was used to measure the
$^{113}$In($\alpha,\gamma$) and $^{113}$In($\alpha$, n) reactions cross-section
near the astrophysical energies. Theoretical statistical model calculations
were performed with different nuclear input parameters and compared with the
experimental results. An appropriate $\alpha$-optical potential has been
identified from the ($\alpha,\gamma$) and ($\alpha$, n) fitting, which provides
the major source of uncertainty in the statistical model calculations. The
other nuclear input parameters like level density, and $\gamma$-ray strength
function were also constrained for theoretical calculations.
$^{113}$In($\alpha,\gamma$)$^{117}$Sb and $^{117}$Sb($\alpha,\gamma$)$^{113}$In
reaction rates were calculated using best-fitted input parameters.
