## Abstract

Metric dimension or location number is a generalization of affine dimension to arbitrary metric spaces (provided a resolving set exists). Let F be a family of connected graphs G_{n}: F = (G_{n})_{n≥1} depending on n as follows: the order |V(G)| = φ(n) and. If there exists a constant C > 0 such that dim(G_{n}) ≤ C for every n ≥ 1 then we shall say that F has bounded metric dimension, otherwise F has unbounded metric dimension. If all graphs in F have the same metric dimension (which does not depend on n), F is called a family with constant metric dimension. In this paper, we study the metric dimension of quasi flower snarks, generalized antiprism and cartesian product of square cycle and path. We prove that these classes of graphs have constant or bounded metric dimension. It is natural to ask for characterization of graphs classes with respect to the nature of their metric dimension. It is also shown that the exchange property of the bases in a vector space does not hold for minimal resolving sets of quasi flower snarks, generalized prism and generalized antiprism.

Original language | English |
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Pages (from-to) | 1665-1674 |

Number of pages | 10 |

Journal | Applied Mathematics and Information Sciences |

Volume | 8 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jul 2014 |

Externally published | Yes |

## Keywords

- Basis
- Exchange property
- Metric dimension
- Quasi flower snark
- Resolving set

## ASJC Scopus subject areas

- Analysis
- Numerical Analysis
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics