Metric Dimension of the Möbius Ladder

Abstract

It is claimed in [13] that the metric dimension of the Möbius ladder \(M_n\) is \(3\) when \(n \not\equiv 2 \pmod{8}\), but it is wrong; we give a counterexample when \(n \equiv 6 \pmod{8}\). In this paper, we not only give the correct metric dimension in this case but also solve the open problem regarding the metric dimension of \(M_n\) when \(n \equiv 2 \pmod{8}\). Moreover, we conclude that \(M_n\) has two subfamilies with constant metric dimensions.