A graph G(V, E) is said to have a vertex prime labeling if its edges can be labeled with distinct integers from {1,2,3,..., |E|} such that for each vertex of degree at least 2, the greatest common divisor of the labels on its incident edges is 1. A graph that admits a vertex prime labeling is called a vertex prime graph. In this paper, we prove that mK_2,3 is a vertex prime graph, where m is any positive integer.