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<p>Given a connected graph <i>G</i>, the equidistant dimension of <i>G</i> represents the cardinality of the smallest set of vertices <i>S</i> of <i>G</i> such that for any two vertices <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(x,y\notin S\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>∉</mo> <mi>S</mi> </mrow> </math></EquationSource> </InlineEquation> there is at least one vertex in <i>S</i> equidistant to both <i>x</i>,&#xa0;<i>y</i> in terms of distances. In this article, we compute the equidistant dimension of some Cartesian product graphs including two-dimensional Hamming graphs, some hypercubes, prisms of cycle, and squared grid graphs.</p>

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Equidistant dimension of Cartesian product graphs

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月20日

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  • Adrià Gispert-Fernández,
  • Juan A. Rodríguez-Velázquez,
  • Ismael G. Yero

摘要

Given a connected graph G, the equidistant dimension of G represents the cardinality of the smallest set of vertices S of G such that for any two vertices \(x,y\notin S\) x , y ∉ S there is at least one vertex in S equidistant to both x, y in terms of distances. In this article, we compute the equidistant dimension of some Cartesian product graphs including two-dimensional Hamming graphs, some hypercubes, prisms of cycle, and squared grid graphs.