Ordered graceful labellings of the 2-star

  title={Ordered graceful labellings of the 2-star},
  author={Richard J. Nowakowski and Carol A. Whitehead},
  journal={Discrete Mathematics},
A variation on the well-known graceful labelling problem for graphs is that of ,nding an ordered graceful labelling. A graceful labelling f :V (T ) → {1; 2; : : : ; n} of a tree T of order n is called ordered graceful if, when the edges of the tree are oriented from the endvertex with larger label to the endvertex with smaller label, then every vertex has either indegree 0 or outdegree 0. In this study, we consider a technique for obtaining ordered graceful labellings of a 2-star T of order n… CONTINUE READING