摘要
In 1977 H. Bodendiek, H. Schumach and H. Wegner proposed the following conjecture: Graphs consisting of a cycle plus one edge joining two nonadjacent vertices are graceful. In this paper, we have proved the following result: For any cycle C_n: x_1x_2… x_(k1)… x_(k2)x_(k1+1) x_(k3)… x_n x_1(k_2-k_1=k-1, 3≤k≤n-3, k_3-k_2=2) when added with two edges x_(k1)x_(k2), x_(k1)x(5), we have obtained a graceful graph.
