2025/03/06 by Tung T. Nguyen, Nguyen, Tung T., Nguyêñ Duy Tân +1 · 1 citation
Mathematics · #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph theory and applications #Number Theory (math.NT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2503.04086
openalex publication_date 2025/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Gcd-graphs represent an interesting and historically important class of integral graphs. Since the pioneering work of Klotz and Sander, numerous incarnations of these graphs have been explored in the literature. In this article, we define and establish some foundational properties of gcd-graphs defined over a general finite commutative ring. In particular, we investigate the connectivity and diameter of these graphs. Additionally, when the ring is a finite symmetric ℤ/n-algebra, we give an explicit description of their spectrum using the theory of Ramanujan sums that gives a unified treatment of various results in the literature.