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

In 1991, Gnanajothi [4] proved that the path graph Pn with n vertex and n -1edge is odd graceful, andthe cycle graph Cm with m vertex and m edges is odd graceful if and only if m even, she proved thecycle graph is not graceful if m odd. In this paper, firstly, we studied the graph m n C èP when m = 4, 6,8,10and then we proved that the graph m n C èP is odd graceful if m is even. Finally, we described analgorithm to label the vertices and the edges of the vertex set ( ) V CmèPn and the edge set ( ) E CmèPn .