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arXiv · 2604.15498

Complemented zero-divisor graph of posets

Anagha Khiste·Ganesh Tarte·Vinayak Joshi
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Abstract

In this paper, we derive a set of equivalent conditions for the zero-divisor graph $\Gamma(Q)$ of a poset $Q$ with $0$ to be complemented, characterizing it in terms of quasi-complemented posets. Furthermore, we prove that the notions of a complemented zero-divisor graph and a uniquely complemented zero-divisor graph coincide for any poset $Q$ with $0$. In addition, we provide both algebraic and topological characterizations for $\Gamma(Q)$ to be a complemented graph. In the final section, we apply these characterizations to the zero-divisor graphs of a reduced (multiplicative) semigroup $S$ with $0$ and the comaximal (ideal) graph of an Artinian ring $R$, and the nonzero component union graph $\mathbb{UG}(\mathbb{V})$ of a finite-dimensional vector space $\mathbb{V}$ over a field $\mathbb{F}$.

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Anagha Khiste, Ganesh Tarte, Vinayak Joshi. 2026-04-16. Complemented zero-divisor graph of posets. https://arxiv.org/abs/2604.15498

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