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<p>In this paper, the generalized blow-up of a Boolean lattice <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L\cong {\textbf {2}}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>L</mi> <mo>≅</mo> <msup> <mrow> <mn mathvariant="bold">2</mn> </mrow> <mi>n</mi> </msup> </mrow> </math></EquationSource> </InlineEquation> 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.</p>

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

  • 期刊论文

  • 发表日期：

    2026年1月19日

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  • Pravin Gadge,
  • Vinayak Joshi

摘要

In this paper, the generalized blow-up of a Boolean lattice \(L\cong {\textbf {2}}^n\) L ≅ 2 n 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.