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arXiv · 2508.01200

Toroidal involutory Cayley graphs

Hamide Keshavarzi·Babak Amini·Afshin Amini·Shahin Rahimi
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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.

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Hamide Keshavarzi, Babak Amini, Afshin Amini, Shahin Rahimi. 2025-08-02. Toroidal involutory Cayley graphs. https://arxiv.org/abs/2508.01200

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