Year: 2026
Type: preprint
Abstract: Let $G$ be the graph on the positive integers in which distinct vertices are adjacent if they differ by one or their quotient in one order is prime. We prove that $6\leq\operatorname{diam}(G)\leq7$ and $4\leq\operatorname{rad}(G)\leq5$. Under Dickson's conjecture for two linear forms, we prove that $\operatorname{diam}(G)=6$ and $\operatorname{rad}(G)=4$.
Source: arXiv (Cornell University)
Institution: Microsoft Research (United Kingdom)
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7215078647