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arXiv · 1907.12670

Minimum coprime graph labelings

Catherine Lee
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Abstract

A coprime labeling of a graph $G$ is a labeling of the vertices of $G$ with distinct integers from $1$ to $k$ such that adjacent vertices have coprime labels. The minimum coprime number of $G$ is the least $k$ for which such a labeling exists. In this paper, we determine the minimum coprime number for several well-studied classes of graphs, including the coronas of complete graphs with empty graphs and the joins of two paths. In particular, we resolve a conjecture of Seoud, El Sonbaty, and Mahran and two conjectures of Asplund and Fox. We also provide an asymptotic for the minimum coprime number of the Erdős-Rényi random graph.

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Catherine Lee. 2020-05-20. Minimum coprime graph labelings. https://arxiv.org/abs/1907.12670

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