  I calculate the quark-gluon vertex of the tensor type
$\Gamma(p,q)=g_3(p,q)p_4 \Slash{\Vec q}$, vector type $g_2(p,q)\Vec q$ and
scalar type $g_1(p,q)$, for a small spacial momentum transfer $q=\bf q$ using
the gauge configuration of the Domain Wall Fermion (DWF) provided by the
RBC-UKQCD collaboration.
  The quark propagator of Coulomb gauge in the cylinder cut, i.e. the four
momentum $p$ is directed along the diagonal of the hyper-cubic space has small
fluctuation and I use this propagator in the evaluation of the operators by
applying the non-perturbative renormalization method.
  The $q$ dependence of the running coupling $\alpha_{s,g_1}(q)$ is compared
with $\alpha_I(q)$ measured by the ghost-gluon vertex in Coulomb gauge and
$\alpha_s(q)$ measured in Landau gauge.
