  In this paper we study non-commutative Yang-Mills theory (NCYM) through its
gravity dual. First it is shown that the gravity dual of an NCYM with self-dual
$\theta$-parameters has a Lagrangian in the form of five-dimensional dilatonic
gravity. Then we use the de-Boer-Verlinde-Verlinde formalism for holographic
renormalization group flows to calculate the coefficient functions in the Weyl
anomaly of the NCYM at low energies under the assumption of potential
dominance, and show that the $C$-theorem holds true in the present case.
