On graceful difference labelings of disjoint unions of circuits

Alain Hertz (1) , Christophe Picouleau (2)

1 GERAD - Groupe d’études et de recherche en analyse des décisions
2 CEDRIC - OC - CEDRIC. Optimisation Combinatoire

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.

Mots clés: Graceful labelings; directed graphs; disjoint unions of circuits

Domaines: Algorithme et structure de données [cs.DS]; Mathématique discrète [cs.DM]; Combinatoire [math.CO]; Informatique [cs]

Alain Hertz, Christophe Picouleau. On graceful difference labelings of disjoint unions of circuits. Open Journal of Discrete Applied Mathematics, 2019, 2 (3), pp.38-55. ⟨10.30538/psrp-odam2019.0021⟩. ⟨hal-02436800⟩