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On graceful difference labelings of disjoint unions of circuits

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.
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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⟩

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