The comparative study of resolving parameters for a family of ladder networks

oleh: Mohra Zayed, Ali Ahmad, Muhammad Faisal Nadeem, Muhammad Azeem

Format: Article
Diterbitkan: AIMS Press 2022-07-01

Deskripsi

For a simple connected graph $ G = (V, E) $, a vertex $ x\in V $ distinguishes two elements (vertices or edges) $ x_1\in V, y_1 \in E $ if $ d(x, x_1)\neq d(x, y_1). $ A subset $ Q_m\subset V $ is a mixed metric generator for $ G, $ if every two distinct elements (vertices or edges) of $ G $ are distinguished by some vertex of $ Q_m. $ The minimum cardinality of a mixed metric generator for $ G $ is called the mixed metric dimension and denoted by $ dim_m(G). $ In this paper, we investigate the mixed metric dimension for different families of ladder networks. Among these families, we consider Möbius ladder, hexagonal Möbius ladder, triangular Möbius ladder network and conclude that all these families have constant-metric, edge metric and mixed metric dimension.