每年專案

## 摘要

Let G be a connected graph with vertex set V, where the distance between two vertices is the length of a shortest path between them. A set S⊆V is [1,2]-resolving if each vertex of G is at most distance-two away from a vertex in S and, given a pair of distinct vertices not in S, either there is a vertex in S adjacent to exactly one member of the given pair, or there are two vertices in S each of which is distance-two from exactly one member of the given pair. The [1,2]-dimension of G is the minimum cardinality of a [1,2]-resolving set of G. In this paper, we study the [1,2]-dimension of graphs by proving that the [1,2]-dimension problem is an NP-complete problem, and determine the [1,2]-dimension of some classes of graphs, such as paths, cycles, and full k-ary trees. We also introduce a generalization of metric dimension of which the (original) metric dimension and the [1,2]-dimension, as well as other metric dimension variants in the literature, are special instances.

原文 | ???core.languages.en_GB??? |
---|---|

頁（從 - 到） | 232-245 |

頁數 | 14 |

期刊 | Discrete Applied Mathematics |

卷 | 337 |

DOIs | |

出版狀態 | 已出版 - 15 10月 2023 |

## 指紋

深入研究「[1,2]-dimension of graphs」主題。共同形成了獨特的指紋。## 專案

- 1 已完成