## Abstract

When there is a difference in the distance between two vertices in a simple linked graph, then a vertex x resolves both u and v. If at least one vertex in S distinguishes each pair of distinct vertices in G, then a set S of vertices in G is referred to as a resolving set. G's metric dimension is the minimum number of vertices required in a resolving set. A subset S of vertices in a simple connected graph is called an edge metric generator if each vertex can tell any two distinct edges e_{1} and e_{2} apart by their respective distances from each other. The edge metric dimension (EMD), denoted as dim_{e}(G), is the smallest cardinality of such a subset S that serves as an edge metric generator for G. The primary objective of this study is to investigate the edge metric dimension (EMD) of hexagonal boron nitride and carbon nanotube structures.

Original language | English |
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Pages (from-to) | 2055-2072 |

Number of pages | 18 |

Journal | European Journal of Pure and Applied Mathematics |

Volume | 17 |

Issue number | 3 |

DOIs | |

Publication status | Published - 31 Jul 2024 |

## Keywords

- carbon nanotube
- edge metric dimension
- hexagonal boron nitride
- metric basis
- Metric generator