Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Keshavarzi, Hamide, Amini, Babak, Amini, Afshin, Rahimi, Shahin
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417098592
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