MINIMAL DOUBLY RESOLVING SETS OF ANTIPRISM GRAPHS AND MOBIUS LADDERS

Saba Sultan, Martin Baca, Ali Ahmad, Muhammad Imran

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Consider a simple connected graph G = (V(G),E(G)), where V(G) represents the vertex set and E(G) represents the edge set respectively. A subset W of V(G) is called a resolving set for a graph G if for every two distinct vertices x, y ∈V(G), there exist some vertex w ∈W such that d(x,w) 6≠ d(y,w), where d(u, v) denotes the distance between vertices u and v. A resolving set of minimal cardinality is called a metric basis for G and its cardinality is called the metric dimension of G, which is denoted by β(G). A subset D of V(G) is called a doubly resolving set of G if for every two distinct vertices x, y of G, there are two vertices u, v ∈ D such that d(u, x) − d(u, y) 6= d(v, x) − d(v, y). A doubly resolving set with minimum cardinality is called minimal doubly resolving set. This minimum cardinality is denoted by ψ(G). In this paper, we determine the minimal doubly resolving sets for antiprism graphs denoted by An with n ≥ 3 and for Möbius ladders denoted by Mn, for every even positive integer n ≥ 8.

Original languageEnglish
Pages (from-to)457-469
Number of pages13
JournalMiskolc Mathematical Notes
Volume23
Issue number1
DOIs
Publication statusPublished - 2022

Keywords

  • Antiprism graph
  • Metric dimension
  • Minimal doubly resolving set
  • Mobius ladder.
  • Resolving set

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Numerical Analysis
  • Discrete Mathematics and Combinatorics
  • Control and Optimization

Fingerprint

Dive into the research topics of 'MINIMAL DOUBLY RESOLVING SETS OF ANTIPRISM GRAPHS AND MOBIUS LADDERS'. Together they form a unique fingerprint.

Cite this