An Algorithm for Odd Graceful Labeling of the Union of Paths and Cycles

In 1991, Gnanajothi [4] proved that the path graph n P with n vertex and 1 n − edge is odd graceful, and the cycle graph m C 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 m n C P ∪ when 4, 6,8,10 m = and then we proved that the graph m n C P ∪ is odd graceful if m is even. Finally, we described an algorithm to label the vertices and the edges of the vertex set ( ) m n V C P ∪ and the edge set ( ) m n E C P ∪ .