English

On graceful difference labelings of disjoint unions of circuits

Combinatorics 2019-08-30 v1

Abstract

A graceful difference labeling (gdl for short) of a directed graph G with vertex set V is a bijection f between V and {1,...,|V|} such that, when each arc uv is assigned the difference label f(v)-f(u), the resulting arc labels are distinct. We conjecture that all disjoint unions of circuits have a gdl, except in two particular cases. We prove partial results which support this conjecture.

Keywords

Cite

@article{arxiv.1908.11300,
  title  = {On graceful difference labelings of disjoint unions of circuits},
  author = {Alain Hertz and Christophe Picouleau},
  journal= {arXiv preprint arXiv:1908.11300},
  year   = {2019}
}

Comments

21 pages,15 figures, 9 tables