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

AIMS Mathematics

article

Mohra Zayed¹  Ali Ahmad²  Muhammad Faisal Nadeem³  Muhammad Azeem⁴ 

[1] Mathematics Department, College of Science, King Khalid University;College of Computer Science & Information Technology Jazan University;Department of Mathematics, COMSATS University Islamabad, Lahore Campus;Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University Lahore

关键词: Möbius ladder network;    hexagonal Möbius ladder network;    triangular Möbius ladder network;    mixed metric dimension;    mixed metric generator;   

DOI  :  10.3934/math.2022908

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

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.

【 授权许可】

CC BY