Toroidal involutory Cayley graphs

2025/08/02 by Keshavarzi, Hamide, Babak Amini, Amini, Babak +4 · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Finite Group Theory Research #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2508.01200

openalex publication_date 2025/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose that R is a finite commutative ring with identity. The involutory Cayley graph \G(R) of R is the graph whose vertices are the elements of R, and two distinct vertices x and y are adjacent if and only if (x-y)²=1. In this paper, we classify all rings R for which \G(R) is a toroidal graph, that is, a graph that can be embedded on a torus.

Citations

• Well-covered Unit Graphs of Finite Rings
• On the Cayley graph of a commutative ring with respect to its\n zero-divisors

Cited by

• Involutory Cayley graphs of polynomial and power series rings over the ring of integers modulo n

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