## Abstract

Metric dimension 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 {pipe}V(G){pipe}=φ(n) and (Formula presented.) 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. 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 properties of of some classes of convex polytopes having pendent edges with respect to their metric dimension.

Original language | English |
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Pages (from-to) | 295-307 |

Number of pages | 13 |

Journal | AKCE International Journal of Graphs and Combinatorics |

Volume | 10 |

Issue number | 3 |

Publication status | Published - Oct 2013 |

Externally published | Yes |

## Keywords

- Basis
- Convex polytope
- Metric dimension
- Pendant
- Plane graph
- Resolving set

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics