## Abstract

Let G = (V, E) be a connected graph and d(u, v) denote the distance between the vertices u and v in G. A set of vertices W resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in W. A metric dimension of G is the minimum cardinality of a resolving set of G and is denoted by dim(G). Let J_{2n,m} be a m-level gear graph obtained by m-level wheel graph W_{2n,m} ≅ mC_{2n} + k_{1} by alternatively deleting n spokes of each copy of C_{2n} and J_{3n} be a generalized gear graph obtained by alternately deleting 2n spokes of the wheel graph W_{3n}. In this paper, the metric dimension of certain gear graphs J_{2n,m} and J_{3n} generated by wheel has been computed. Also this study extends the previous result given by Tomescu et al. in 2007.

Original language | English |
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Article number | 209 |

Journal | Symmetry |

Volume | 10 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jun 1 2018 |

## Keywords

- Basis
- Gear graph
- Generalized gear graph
- Metric dimension
- Resolving set

## ASJC Scopus subject areas

- Computer Science (miscellaneous)
- Chemistry (miscellaneous)
- General Mathematics
- Physics and Astronomy (miscellaneous)