In 1991, Gnanajothi [4] proved that the path graph P_n with n vertex and n-1
edge is odd graceful, and the cycle graph C_m with m vertex and m edges is odd
graceful if and only if m even, she proved the cycle graph is not graceful if m
odd. In this paper, firstly, we studied the graph C_m βͺ P_m when m = 4,
6,8,10 and then we proved that the graph C_ βͺ P_n is odd graceful if m is
even. Finally, we described an algorithm to label the vertices and the edges of
the vertex set V(C_m βͺ P_n) and the edge set E(C_m βͺ P_n).Comment: 9 Pages, JGraph-Hoc Journa