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arXiv · 2608.27381

Boxicity and Threshold Dimension of Zero Divisor Graphs

Marco Caoduro·Meike Neuwohner
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Abstract

The zero divisor graph $\Gamma(R)$ of a finite commutative ring $R$ has as vertices the non-zero zero divisors of $R$, with an edge between two elements exactly when their product is zero. We determine the boxicity and threshold dimension of $\Gamma(R)$ for two classes of finite commutative rings: reduced rings and quotients of principal ideal domains. Our proofs use a new combinatorial gadget, the integral covering graph, that captures the structure shared by both ring families and generalizes the disjointness graph on subsets of $[n]$, where two subsets are adjacent if and only if they are disjoint. In doing so, we answer two questions recently posed by L.~Sunil Chandran and Suraj Kumar Sahoo in Boxicity of Zero Divisor Graphs, Discrete Applied Mathematics 391 (2026).

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Marco Caoduro, Meike Neuwohner. 2026-08-27. Boxicity and Threshold Dimension of Zero Divisor Graphs. https://arxiv.org/abs/2608.27381

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