A proof of the Multiplicative 1-2-3 Conjecture

Julien Bensmail (1) , Hervé Hocquard (2) , Dimitri Lajou (2) , Eric Sopena (2)

1 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

We prove that the product version of the 1-2-3 Conjecture, raised by Skowronek-Kaziów in 2012, is true. Namely, for every connected graph with order at least 3, we can assign labels 1,2,3 to the edges so that no two adjacent vertices are incident to the same product of labels.

Mots clés: 1-2-3 Conjecture; product version; labels 1-2-3

Domaines: Mathématique discrète [cs.DM]

Julien Bensmail, Hervé Hocquard, Dimitri Lajou, Eric Sopena. A proof of the Multiplicative 1-2-3 Conjecture. CALDAM 2022 - 8th Annual International Conference on Algorithms and Discrete Applied Mathematics, Feb 2022, Puducherry, India. ⟨10.1007/978-3-030-95018-7_1⟩. ⟨hal-03427170⟩