A graph G of size q is odd-graceful, if there is an injection f from V(G) to {0, 1, 2, …, 2q-1} such that, when each edge xy is assigned the label or weight | f(x) - f(y)|, the resulting edge labels are {1, 3, 5, …, 2q-1}. This definition was introduced in 1991 by Gnanajothi [1] who proved that the graphs obtained by joining a single pendant edge to each vertex of are odd graceful, if and only if n is even. In this paper we generalize Gnanajothi's result on cycles by showing that the graphs obtained by joining m pendant edges to each vertex of Cn are odd graceful if and only if n is even.