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PreprintCC BY 4.0arXiv

Diameter and radius of an additive-multiplicative graph

  • Yi Hu
  • Nan Yang
Open at sourcePDFDOICite

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≤diam(G)≤7 and 4≤rad(G)≤5. Under Dickson's conjecture for two linear forms, we prove that diam(G)=6 and rad(G)=4.

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Cite

BibTeXRIS
BibTeX
@misc{hu2026diameter,
  title = {{Diameter and radius of an additive-multiplicative graph}},
  author = {Yi Hu and Nan Yang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39347},
  eprint = {2609.39347},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39347},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Diameter and radius of an additive-multiplicative graph
AU  - Yi Hu
AU  - Nan Yang
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.39347
UR  - https://arxiv.org/abs/2609.39347
AB  - 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≤diam(G)≤7 and 4≤rad(G)≤5. Under Dickson's conjecture for two linear forms, we prove that diam(G)=6 and rad(G)=4.
ER  -