On the strong metric dimension of the zero-divisor graph of a lattice

2024/09/08 by Pravin Gadge, Gadge, Pravin, Vinayak Joshi +1 · 1 citation
Computer Science · Mathematics · #05C17 #05C25 #06A07 #13A70 #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2409.05146

openalex publication_date 2024/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, the generalized blow-up of a Boolean lattice L≅ 2ⁿ using finite chains is introduced. Also, we compute the strong metric dimension of the zero-divisor graph of the blow-up of a Boolean lattice. These results are applied to calculate the strong metric dimension of the comaximal graph, the comaximal ideal graph, the zero-divisor graph of a reduced ring, and the component graph of a vector space.

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• On the strong metric dimension of the complement of the zero-divisor graph of a lattice

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