Equidistant dimension of Cartesian product graphs

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 $$x,y\notin S$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:mi>y</mml:mi> <mml:mo>∉</mml:mo> <mml:mi>S</mml:mi> </mml:mrow> </mml:math> 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.