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arXiv · 2005.06308

Hamiltonicity of a coprime graph

M. H. Bani Mostafa A.·Ebrahim Ghorbani
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Abstract

The $k$-coprime graph of order $n$ is the graph with vertex set $\{k, k+1, \ldots, k+n-1\}$ in which two vertices are adjacent if and only if they are coprime. We characterize Hamiltonian $k$-coprime graphs. As a particular case, two conjectures by Tout, Dabboucy, Howalla (1982) and by Schroeder (2019) on prime labeling of $2$-regular graphs follow. A prime labeling of a graph with $n$ vertices is a labeling of its vertices with distinct integers from $\{1, 2,\ldots , n\}$ in such a way that the labels of any two adjacent vertices are relatively prime.

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M. H. Bani Mostafa A., Ebrahim Ghorbani. 2020-08-07. Hamiltonicity of a coprime graph. https://arxiv.org/abs/2005.06308

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