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arXiv · 2108.10554

A proof of the Multiplicative 1-2-3 Conjecture

Julien Bensmail·Hervé Hocquard·Dimitri Lajou·Éric Sopena
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Abstract

We prove that the product version of the 1-2-3 Conjecture, raised by Skowronek-Kazi{\'o}w in 2012, is true. Namely, for every connected graph with order at least 3, we prove that we can assign labels 1,2,3 to the edges in such a way that no two adjacent vertices are incident to the same product of labels.

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Julien Bensmail, Hervé Hocquard, Dimitri Lajou, Éric Sopena. 2021-08-24. A proof of the Multiplicative 1-2-3 Conjecture. https://arxiv.org/abs/2108.10554

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