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A general solution for the 1-2 conjecture using real numbers (2506.14253v2)
Published 17 Jun 2025 in math.CO
Abstract: The 1-2 conjecture posits that for every graph, weights from ${1,2}$ can be assigned to its vertices and edges so that adjacent vertices have distinct weighted degrees. This paper demonstrates that any set of two distinct real numbers ${a,b}$ can achieve the same goal, thereby confirming the 1-2 conjecture in a broader context.
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