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arXiv · 2512.07672

Equidistant dimension of Cartesian product graphs

Adria Gispert-Fernandez·Juan A. Rodriguez-Velazquez·Ismael G. Yero
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Abstract

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 $x,y\notin S$ 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.

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Adria Gispert-Fernandez, Juan A. Rodriguez-Velazquez, Ismael G. Yero. 2025-12-08. Equidistant dimension of Cartesian product graphs. https://arxiv.org/abs/2512.07672

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