A proof of the Multiplicative 1-2-3 Conjecture

08/24/2021

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by   Julien Bensmail, et al.

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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 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.