2024/10/26 by Gergő Batta, Lajos Hajdu, Batta, Gergő +3 · 1 citation
Mathematics · #05C15 #05C42 #11D09 #11D25 #11D75 #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2410.20120
openalex publication_date 2024/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Diophantine tuples are of ancient and modern interest, with a huge literature. In this paper we study Diophantine graphs, i.e., finite graphs whose vertices are distinct positive integers, and two vertices are linked by an edge if and only if their product increased by one is a square. We provide various results for Diophantine graphs, including extendability properties, lower- and upper bounds for the maximum number of edges and chromatic numbers.