  In this work, we analyze the strong vertices $\Sigma_{c}\Delta D^{*}$ and
$\Sigma_{b}\Delta B^{*}$ using the three-point QCD sum rules under the tensor
structures $i\epsilon^{\rho\tau\alpha\beta}p_{\alpha}p'_{\beta}$,
$p^{\rho}p'^{\tau}$ and $p^{\rho}p^{\tau}$. We firstly calculate the momentum
dependent strong coupling constants $g(Q^{2})$ by considering contributions of
the perturbative part and the condensate terms $\langle\overline{q}q\rangle$,
$\langle g_{s}^{2}GG \rangle$, $\langle\overline{q}g_{s}\sigma Gq\rangle$ and
$\langle\overline{q}q\rangle^{2}$. By fitting these coupling constants into
analytical functions and extrapolating them into time-like regions, we then
obtain the on-shell values of strong coupling constants for these vertices. The
results are $g_{1\Sigma_{c}\Delta D^{*}}=5.13^{+0.39}_{-0.49}$ GeV$^{-1}$,
$g_{2\Sigma_{c}\Delta D^{*}}=-3.03^{+0.27}_{-0.35}$ GeV$^{-2}$,
$g_{3\Sigma_{c}\Delta D^{*}}=17.64^{+1.51}_{-1.95}$ GeV$^{-2}$,
$g_{1\Sigma_{b}\Delta B^{*}}=20.97^{+2.15}_{-2.39}$ GeV$^{-1}$,
$g_{2\Sigma_{b}\Delta B^{*}}=-11.42^{+1.17}_{-1.28}$ GeV$^{-2}$ and
$g_{3\Sigma_{b}\Delta B^{*}}=24.87^{+2.57}_{-2.82}$ GeV$^{-2}$. These strong
coupling constants are important parameters which can help us to understand the
strong decay behaviors of hadrons.
