Abstract : A graceful difference labeling (gdl for short) of a directed graph G with vertex set V is a bijection f : V → {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.
Alain Hertz, Christophe Picouleau. On graceful difference labelings of disjoint unions of circuits. Open Journal of Discrete Applied Mathematics, PSR Press, 2019, 2 (3), pp.38-55. ⟨10.30538/psrp-odam2019.0021⟩. ⟨hal-02436800⟩