Rings whose total graphs have genus at most one

Hamid Reza Maimani, Cameron Wickham, Siamak Yassemi

Let $R$ be a commutative ring with $\mathbb{Z}(R)$ its set of zero-divisors. In this paper, we study the total graph of $R$, denoted by $\T(Γ(R))$. It is the (undirected) graph with all el…