Volume 35 • Number 1 • 2012   • On Gracefulness of Directed Trees with Short Diameters Bing Yao, Ming Yao and Hui Cheng Abstract. Graceful labelling is studied on undirected graphs since graceful graphs can be used in some $H$-decomposition problems. In this note, we investigate the directed graceful problem for many orientations of undirected trees with short diameters, and provide some directed trees that deny any digraceful labelling. 2010 Mathematics Subject Classification: 05C78. Full text: PDF