Generalized M\"{o}bius Ladder and Its Metric Dimension

TL;DR

This paper introduces a new class of graphs called generalized Möbius ladders, analyzes their metric dimensions, and identifies how these dimensions vary with the parity of parameters, revealing two subfamilies with constant metric dimensions.

Contribution

It defines the generalized Möbius ladder $M_{m,n}$ and determines its metric dimension, highlighting differences based on even and odd parameter values.

Findings

Generalized Möbius ladder $M_{m,n}$ defined and analyzed.

Metric dimension depends on parity of $m$ and $n$.

Two subfamilies with constant metric dimensions identified.

Abstract

In this paper we introduce generalized M\"{o}bius ladder $M_{m,n}$ and give its metric dimension. Moreover, it is observed that, depending on even and odd values of $m$ and $n$, it has two subfamilies with constant metric dimensions.