Symmetry (Dec 2023)
Classification of Genus Three Zero-Divisor Graphs
Abstract
In this paper, we consider the problem of classifying commutative rings according to the genus number of its associating zero-divisor graphs. The zero-divisor graph of R, where R is a commutative ring with nonzero identity, denoted by Γ(R), is the undirected graph whose vertices are the nonzero zero-divisors of R, and the distinct vertices x and y are adjacent if and only if xy=0. Here, we classify the local rings with genus three zero-divisor graphs.
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