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Zero-divisor graph

The zero-divisor graph of $\mathbb {Z} _{2}\times \mathbb {Z} _{4}$ , the only possible zero-divisor graph that is a tree but not a star

In mathematics, and more specifically in combinatorial commutative algebra, a zero-divisor graph is an undirected graph representing the zero divisors of a commutative ring. It has elements of the ring as its vertices, and pairs of elements whose product is zero as its edges.^[1]

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