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A graph G = ( V, E ) with n vertices is said to admit prime labeling if its vertices can be labeled with distinct positive integers not exceed n such that the label of each pair of adjacent vertices are relatively prime. A graph G which admits prime labeling is called a prime graph. In this paper, we investigate prime labeling for some classes of graph. In particular, we discuss on prime labeling of middle graph of cycle , when n is even (or) odd.