In this paper, we holographically study the renormalization group (RG) flow in a three-dimensional Einstein-dilaton gravity with a specific scalar potential, which permits several different types of the RG flow with nontrivial beta functions. By using the intrinsic parameter of the potential, we classify the possible holographic RG flows and examine their physical features. Using the Ryu-Takayanagi formulation, furthermore, we investigate how the c function of the entanglement entropy behaves along with the RG flow numerically. We show that the entanglement c function monotonically decreases even in the cases with a nontrivial beta function. For checking the consistency, we also compare the result of the entanglement entropy with the c function derived from the holographic renormalization procedure.
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