# The Zero-Divisor Graph Problem

Research output: Other contribution

## Abstract

Abstract: Let $S$ be a commutative semigroup with $0$ element. A nonzero element $a\in S$ is called a zero-divisor if there exists a nonzero element $b\in S$ so that $ab=0$. The zero-divisor graph, $\Gamma (S)$ is the simple graph whose vertices are given by the nonzero zero-divisors of $S$ where two distinct vertices, $a$ and $b$, are adjacent in case $ab=0$ in $S$. We will begin with a discussion of the history of this construction and foundational results, including examples. We conclude with some very recent results, other zero divisor graph constructions, and some open questions.
Original language English Published - Nov 2019

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