## Abstract

An ordered set W= { w_{1},.. , w_{k}} ⫅ V(G) of vertices of G is called a resolving set or locating set for G if every vertex is uniquely determined by its vector of distances to the vertices in W. A resolving set of minimum cardinality is called a metric basis for G and this cardinality is the metric dimension or location number of G, denoted by β(G). The metric dimension of certain wheel related graphs has been studied recently in [22]. In this paper, we extend this study to infinite classes of convex polytopes generated by wheel related graphs. We prove that these infinite classes of convex polytopes generated by wheel related graphs have unbounded metric dimension. It is natural to ask for the characterization of graphs with unbounded metric dimension.

Original language | English |
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Pages (from-to) | 10-30 |

Number of pages | 21 |

Journal | Acta Mathematica Hungarica |

Volume | 149 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jun 2016 |

Externally published | Yes |

## Keywords

- basis
- convex polytope
- metric dimension
- resolving set
- wheel related graph

## ASJC Scopus subject areas

- Mathematics(all)