About the Bodendiek’s conjecture of graceful graph. (Chinese. English summary) Zbl 0564.05053
In 1977, H. Bodendiek, H. Schumacher and H. Wegner [Elemente Math. 32, 49-58 (1977; Zbl 0361.05050)] proposed the following conjecture: The graphs consisting of a cycle plus one edge joining two nonadjacent vertices are graceful. In this paper, we prove the following result. For any cycle \(C_ n\) the addition of one edge joining two non adjacent vertices results in the graceful graph \(C'_ n\).
